This paper considers the estimation of a nonparametric regression model with randomly right-censored data. To estimate the model, rational (Padé) approximation based on truncated total least squares (P-TTLS) is used as a smoothing method.... more
This paper considers the estimation of a nonparametric regression model with randomly right-censored data. To estimate the model, rational (Padé) approximation based on truncated total least squares (P-TTLS) is used as a smoothing method. Because of censored, data points cannot be used directly in modeling process, a data transformation is needed for overcoming this problem. As known, synthetic data transformation assigns censored points as zero and gives additional magnitudes to uncensored ones associated with Kaplan-Meier distribution of the censored dataset. Thus, the differences between censored and uncensored observations grow which causes a kind of spatial variation in the shape of data. In this paper, to bring a solution to this problematic situation, P-TTLS is used that works well on spatial variation. Also, to see the performance of the P-TTLS on censored data modeling, a simulation study is carried out and it is compared with the benchmarked kernel smoothing (B-KS) method ...
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This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case:... more
This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan–Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data’s structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method ...
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This paper aims to solve the problem of fitting a nonparametric regression function with right-censored data. In general, issues of censorship in the response variable are solved by synthetic data transformation based on the Kaplan–Meier... more
This paper aims to solve the problem of fitting a nonparametric regression function with right-censored data. In general, issues of censorship in the response variable are solved by synthetic data transformation based on the Kaplan–Meier estimator in the literature. In the context of synthetic data, there have been different studies on the estimation of right-censored nonparametric regression models based on smoothing splines, regression splines, kernel smoothing, local polynomials, and so on. It should be emphasized that synthetic data transformation manipulates the observations because it assigns zero values to censored data points and increases the size of the observations. Thus, an irregularly distributed dataset is obtained. We claim that adaptive spline (A-spline) regression has the potential to deal with this irregular dataset more easily than the smoothing techniques mentioned here, due to the freedom to determine the degree of the spline, as well as the number and location ...
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Research Interests: Mathematics, Applied Mathematics, Comparative Study, Optimization, Model Selection, and 14 moreMixed Effect Model, Selection Criteria, Cross Validation, Sample Size, Smoothing, Mathematical Optimization, Simulation Study, Akaike Information Criterion, Numerical Analysis and Computational Mathematics, Restricted Maximum Likelihood, Risk estimation, Information Criteria, Smoothing Spline, and Smoothing parameter
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In statistical analyses, especially those using a multiresponse regression model approach, a mathematical model that describes a functional relationship between more than one response variables and one or more predictor variables is often... more
In statistical analyses, especially those using a multiresponse regression model approach, a mathematical model that describes a functional relationship between more than one response variables and one or more predictor variables is often involved. The relationship between these variables is expressed by a regression function. In the multiresponse nonparametric regression (MNR) model that is part of the multiresponse regression model, estimating the regression function becomes the main problem, as there is a correlation between the responses such that it is necessary to include a symmetric weight matrix into a penalized weighted least square (PWLS) optimization during the estimation process. This is, of course, very complicated mathematically. In this study, to estimate the regression function of the MNR model, we developed a PWLS optimization method for the MNR model proposed by a previous researcher, and used a reproducing kernel Hilbert space (RKHS) approach based on a smoothing ...
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This paper proposes a semiparametric local polynomial estimator for modelling agricultural time-series. We consider the modelling of the crop yield variable according to determined financial risk factors in Turkey. The derivation of a... more
This paper proposes a semiparametric local polynomial estimator for modelling agricultural time-series. We consider the modelling of the crop yield variable according to determined financial risk factors in Turkey. The derivation of a semiparametric local polynomial estimator is provided with its fundamental statistical properties to estimate the semiparametric time-series model. This paper attaches importance to precision agriculture (PA) and therefore a local polynomial technique is considered due to some advantages it has over alternative methods. The introduced estimator provides less estimation risk, involving both parametric and nonparametric components that allow the estimator to represent the data structure better. From that, it can be said that the proposed estimator and model is beneficial to agricultural researchers for financial decision-making processes.
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Smoothing methods that use basis functions with penalization can be formulated as fits in formlinear mixed effects models. This allows s uch models to be fitted using sta ndard mixed models structures. In this paper we provide an... more
Smoothing methods that use basis functions with penalization can be formulated as fits in formlinear mixed effects models. This allows s uch models to be fitted using sta ndard mixed models structures. In this paper we provide an estimation and inference for linear mixed models using restrict- ed maximum likelihood and penalized spline smoothing, and describe the connection between the two. To this end, a real data example is considered and model is fitted in R using diff erent package. We see that penalized spline smoothing expressed in form of linear mixed model gives the better results than standard mixed effects model.
In this paper, the proposed estimator for the unknown nonparametric regression function is a Nadarya-Watson (Nadarya, 1964; Watson, 1964) type kernel estimator. In this estimation procedure, the censored observations are replaced by... more
In this paper, the proposed estimator for the unknown nonparametric regression function is a Nadarya-Watson (Nadarya, 1964; Watson, 1964) type kernel estimator. In this estimation procedure, the censored observations are replaced by synthetic data points based on Kaplan-Meier estimator. As known performance of the kernel estimator depends on the selection of a bandwidth parameter. To get an optimum parameter we have considered six selection methods such as the improved version of Akaike information criterion (AICc), Bayesian information criterion (BIC), generalized cross validation (GCV), risk estimation with classical pilots (RECP), Mallow’s Cp criterion and restricted empirical likelihood (REML), respectively. In addition, we discuss the behavior of the estimators obtained by these selection methods under different configurations of the censoring level and sample sizes. Simulation and real lifetime data results are presented to evaluate and compare the performance of the selection...
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Smoothing methods that use basis functions with penalization can be formulated as fits in formlinear mixed effects models. This allows s uch models to be fitted using sta ndard mixed models structures. In this paper we provide an... more
Smoothing methods that use basis functions with penalization can be formulated as fits in formlinear mixed effects models. This allows s uch models to be fitted using sta ndard mixed models structures. In this paper we provide an estimation and inference for linear mixed models using restrict- ed maximum likelihood and penalized spline smoothing, and describe the connection between the two. To this end, a real data example is considered and model is fitted in R using diff erent package. We see that penalized spline smoothing expressed in form of linear mixed model gives the better results than standard mixed effects model.
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In this article, we introduce a modified ridge type estimator for the vector of parameters in a partially linear model. This estimator is a generalization of the well-known Speckman’s approach and is based on smoothing splines method.... more
In this article, we introduce a modified ridge type estimator for the vector of parameters in a partially linear model. This estimator is a generalization of the well-known Speckman’s approach and is based on smoothing splines method. Most important in the implementation of this method is the choice of the smoothing parameter. Many Criteria of selecting smoothing parameters such as improved version of Akaike information criterion (AICc), generalized cross-validation (GCV), cross-validation (CV), Mallows’ Cp criterion, risk estimation using classical pilots (REC) and Bayes information criterion (BIC) are developed in literature. In order to illustrate the ideas in the paper, a real data example and a Monte Carlo simulation study are carried out. Thus, the appropriate selection criteria are provided for a suitable smoothing parameter selection.
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Abstract In this paper, we try to investigate how the current account to gross domestic product (CAGDP) ratio in Turkey reacts to variations in the real effective exchange rate (REER) over the period of 1991: Q4-2007: Q3. For this... more
Abstract In this paper, we try to investigate how the current account to gross domestic product (CAGDP) ratio in Turkey reacts to variations in the real effective exchange rate (REER) over the period of 1991: Q4-2007: Q3. For this purpose, we consider two different ...
Research Interests: Mathematics, Econometrics, Nonparametric Statistics, Industrial Engineering, Economic Indicators, and 12 moreRegression Analysis, Nonparametric Regression, Shape, Predictive models, Smoothing, Spline, Regression Model, Parametric Statistics, Computer, Current Account, Gross Domestic Product, and Smoothing Spline
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Research Interests: Mathematics and Ridge
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This paper considers the role of influence diagnostics in the partially linear regression models, y = Xβ +f +ε. An influential observation on the estimator of the coefficient vector may not be influential on that of the nonparametric... more
This paper considers the role of influence diagnostics in the partially linear regression models, y = Xβ +f +ε. An influential observation on the estimator of the coefficient vector may not be influential on that of the nonparametric component f(x), and vice versa. Also, an observation which is not influential on either parametric or non-parametric component may be influential on the estimator of the mean response. So, we focus on influence measures for each estimator β, f, and the mean response Xβ +f. In the literature, the Cook's distance is used to detect influential observation in partially linear models. In certain types of data sets, it is quite common an unusual observation or a small subset using Dffits, Dfbetas, and CovRatio statistics. Therefore, in our study, Dffits, Dfbetas, and CovRatio are proposed to identify any influential observation in the partially linear regression models. These measures are discussed on each of which measures the effect of detecting an inf...
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It is known that parametric and nonparametric methods are used for nonlinear time series. In recently, hybrid models are also considered in time series forecasting. In this paper we present the hybrid models whose components are... more
It is known that parametric and nonparametric methods are used for nonlinear time series. In recently, hybrid models are also considered in time series forecasting. In this paper we present the hybrid models whose components are parametric and nonparametric models. Of the parametric methods, autoregressive (AR) model and self-threshold value (SETAR) model and, of the nonparametric methods, additive regression model (ARM) and hybrid AR&AAR, AR&SETAR, AAR&SETAR, SETAR&AR, SETAR&AAR and AAR&AR models are used in this study. In this context, back fitting algorithm based on smoothing spline method in the existing literature is discussed. A comparison has been made for the performance of the models obtained for the export volume index numbers and domestic producer price index data for Turkey. These results showed that AAR&SETAR hybrid model has denoted the best performance among the all models in time series forecasting.
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In this study, firstly we will define a right censored data. If we say shortly right-censored data is censoring values that above the exact line. This may be related with scaling device. And then we will use response variable acquainted... more
In this study, firstly we will define a right censored data. If we say shortly right-censored data is censoring values that above the exact line. This may be related with scaling device. And then we will use response variable acquainted from right-censored explanatory variables. Then the linear regression model will be estimated. For censored data’s existence, Kaplan-Meier weights will be used for the estimation of the model. With the weights regression model will be consistent and unbiased with that. And also there is a method for the censored data that is a semi parametric regression and this method also give useful results for censored data too. This study also might be useful for the health studies because of the censored data used in medical issues generally.
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The purpose of this study is to estimate the right-censored nonparametric model with kernel smoothing method. To consider the censorship, we used Kaplan-Meier estimator proposed by Stute (1993). In nonparametric statistics, a kernel... more
The purpose of this study is to estimate the right-censored nonparametric model with kernel smoothing method. To consider the censorship, we used Kaplan-Meier estimator proposed by Stute (1993). In nonparametric statistics, a kernel smoothing method needs a smoothing parameter which is also called as a bandwidth parameter. In this study, we choose the bandwidth parameter by using three selection methods such as improved version of Akaike information criterion (AICc), Risk estimation using classical pilots (RECP) and Generalized cross-validation(GCV) method, respectively. For this purpose, a Monte-Carlo simulation study is performed to illustrate which selection criterion gives the best estimation for different sample sizes and censoring levels. Key-Words: Kernel Smoothing, Kaplan-Meier Estimator, Nonparametric Regression, Censored data
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... Özet Bu çalişma, Türkiye'de 2003-2009 yillari arasinda aylik olarak ortaya çikan ÜFE ve TÜFE bazli reel efektif döviz kuru değerleri için parametrik olmayan (nonpa-rametrik) regresyon kestiricilerinin bazi performans ölçülerinin... more
... Özet Bu çalişma, Türkiye'de 2003-2009 yillari arasinda aylik olarak ortaya çikan ÜFE ve TÜFE bazli reel efektif döviz kuru değerleri için parametrik olmayan (nonpa-rametrik) regresyon kestiricilerinin bazi performans ölçülerinin bir değerlendir-mesini yapmaktadir. ...
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This paper focuses on nonparametric regression modeling of time-series observations with data irregularities, such as censoring due to a cutoff value. In general, researchers do not prefer to put up with censored cases in time-series... more
This paper focuses on nonparametric regression modeling of time-series observations with data irregularities, such as censoring due to a cutoff value. In general, researchers do not prefer to put up with censored cases in time-series analyses because their results are generally biased. In this paper, we present an imputation algorithm for handling auto-correlated censored data based on a class of autoregressive nonparametric time-series model. The algorithm provides an estimation of the parameters by imputing the censored values with the values from a truncated normal distribution, and it enables unobservable values of the response variable. In this sense, the censored time-series observations are analyzed by nonparametric smoothing techniques instead of the usual parametric methods to reduce modelling bias. Typically, the smoothing methods are updated for estimating the censored time-series observations. We use Monte Carlo simulations based on right-censored data to compare the performances and accuracy of the estimates from the smoothing methods. Finally, the smoothing methods are illustrated using a meteorological time- series and unemployment datasets, where the observations are subject to the detection limit of the recording tool.
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Abstract In this paper, we propose a Padé-type approximation based on truncated total least squares (P – TTLS) and compare it with three commonly used smoothing methods: Penalized spline, Kernel smoothing and smoothing spline methods that... more
Abstract In this paper, we propose a Padé-type approximation based on truncated total least squares (P – TTLS) and compare it with three commonly used smoothing methods: Penalized spline, Kernel smoothing and smoothing spline methods that have become very powerful smoothing techniques in the nonparametric regression setting. We consider the nonparametric regression model, and discuss how to estimate smooth regression function g where we are unsure of the underlying functional form of g. The Padé approximation provides a linear model with multi-collinearities and errors in all its variables. The P – TTLS method is primarily designed to address these issues, especially for solving error-contaminated systems and ill-conditioned problems. To demonstrate the ability of the method, we conduct Monte Carlo simulations under different conditions and employ a real data example. The outcomes of the experiments show that the fitted curve solved by P – TTLS is superior to and more stable than the benchmarked penalized spline (B – PS), Kernel smoothing (KS) and smoothing spline (SS) techniques.
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ABSTRACT In this work we introduce different modified estimators for the vector parameter and an unknown regression function g in semiparametric regression models when censored response observations are replaced with synthetic data... more
ABSTRACT In this work we introduce different modified estimators for the vector parameter and an unknown regression function g in semiparametric regression models when censored response observations are replaced with synthetic data points. The main idea is to study the effects of several covariates on a response variable censored on the right by a random censoring variable with an unknown probability distribution. To provide the estimation procedure for the estimators, we extend the conventional methodology to censored semiparametric regression using different smoothing methods such as smoothing spline (SS), kernel smoothing (KS), and regression spline (RS). In addition to estimating the parameters of the semiparametric model, we also provide a bootstrap technique to make inference on the parameters. A simulation study is carried out to show the performance and efficiency properties of the estimators and analyse the effects of the different censoring levels. Finally, the performance of the estimators is evaluated by a real right-censored data set.
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This paper introduces an estimation procedure for the right-censored nonparametric regression model using smoothing spline method. In this process, to overcome the censorship problem we used an imputation method based on k-nearest... more
This paper introduces an estimation procedure for the right-censored nonparametric regression model using smoothing spline method. In this process, to overcome the censorship problem we used an imputation method based on k-nearest neighbors (kNN). Among some known censorship solutions, such as Kaplan-Meier weights (Kaplan and Meier, Miller) and Synthetic data transformation (Koul et al.), the most important advantage of the kNN imputation method is that it does not depend on a distribution. After solving the problem of censorship, the most important problem in obtaining the optimal estimation of non1parametric regression function by using smoothing spline will be the selection of the smoothing parameter. In order to achieve this aim, three commonly used criteria such as generalized cross-validation (GCV), Bayesian information criterion (BIC) and risk estimation using classical pilots (RECP) are considered in this study. A Monte-Carlo simulation study and a “kidney infection recurrence” data are carried out to realize the purposes of this study. Thus, it is determined that which selection criterion is more successful in estimating the non-parametric model with right censored data. Obtained results from both simulation and real-world studies show that BIC has remarkable performance among others. Also, it can be seen that GCV is better than BIC for large sample size. RECP has mediocre performance.
Abstract This paper introduces a Padé-type approximation for an unknown regression function in a nonparametric regression model. This newly introduced approximation provides a linear model with multi-collinearities and errors in all its... more
Abstract This paper introduces a Padé-type approximation for an unknown regression function in a nonparametric regression model. This newly introduced approximation provides a linear model with multi-collinearities and errors in all its variables. To deal with these issues, we used the truncated total least squares (TTLS) method. The efficient implementation of a Padé-type method using TTLS depends on choosing a truncation level. To provide an optimum truncation level for this method, we update the conventional parameter selection methods, including the generalized cross validation (GCV), improved version of the Akaike information criterion (AICc), restricted maximum likelihood (REML), Bayesian information criterion (BIC), and Mallows’ Cp criterion. The primary aim of this study is to compare the performances of these level selection methods. A Monte Carlo simulation and a real data example are performed to illustrate the ideas in the paper. The results confirm that the GCV and AICc slightly outperform the other methods, especially when sample sizes are small and large, respectively.
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This paper study about using of nonparametric models for Gross National Product data in Turkey and Stanford heart transplant data. It is discussed two nonparametric techniques called smoothing spline and kernel regression. The main... more
This paper study about using of nonparametric
models for Gross National Product data in Turkey and Stanford heart
transplant data. It is discussed two nonparametric techniques called
smoothing spline and kernel regression. The main goal is to compare
the techniques used for prediction of the nonparametric regression
models. According to the results of numerical studies, it is concluded
that smoothing spline regression estimators are better than those of
the kernel regression.
models for Gross National Product data in Turkey and Stanford heart
transplant data. It is discussed two nonparametric techniques called
smoothing spline and kernel regression. The main goal is to compare
the techniques used for prediction of the nonparametric regression
models. According to the results of numerical studies, it is concluded
that smoothing spline regression estimators are better than those of
the kernel regression.
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ABSTRACT This paper presents a comparative study of different estimations of the partially linear models based on the smoothing spline technique. Performance of this technique greatly depends on the selection of smoothing parameters. Many... more
ABSTRACT This paper presents a comparative study of different estimations of the partially linear models based on the smoothing spline technique. Performance of this technique greatly depends on the selection of smoothing parameters. Many methods of selecting smoothing parameters such as an improved version of Akaike information criterion (AICc), generalized cross-validation (GCV), cross-validation (CV), Mallows’ Cp criterion, risk estimation using classical pilots (REC) and local risk estimation (LRS) are developed in literature. The smoothing parameter selection has been discussed in respect to a smoothing spline implementation in predicting the partially linear model (PLM). To this end, a simulation study has been conducted to evaluate and compare the performance of six selection methods. In this connection, 1000 replications have been performed in simulation for sample sets with different sizes. The AICc method is recommended since it is stable and works well in all simulations. It performs better than other methods especially when the sample sizes are not large.
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ABSTRACT The focus in this paper embraces the hybrid models whose components are nonparametric regression and artificial neural networks. Smoothing spline, regression spline and additive regression models are considered as the... more
ABSTRACT The focus in this paper embraces the hybrid models whose components are nonparametric regression and artificial neural networks. Smoothing spline, regression spline and additive regression models are considered as the nonparametric regression components. Furthermore, various multilayer perceptron algorithms and radial basis function network model are regarded as the artificial neural networks components. The performances of these models are compared by forecasting three real Turkish data sets: Domestic product per capita (GDP), the number of cars produced and the number of tourist arrivals. The results obtained by experimental evaluations show that hybrid models proposed in this paper have performed much better in comparison to hybrid models discussed in literature.
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In this paper, different regression models are obtained to examine relation between house price and house features in Centrum of Eskisehir Province (Turkey). The statistical analyses of this paper indicate that some of explanatory... more
In this paper, different regression models are obtained to examine relation between house price and house features in Centrum of Eskisehir Province (Turkey). The statistical analyses of this paper indicate that some of explanatory variables affect the response variable parametrically and some of them nonparametrically. Therefore, obtained suitable model has both parametric and nonparametric variables and the model is semiparametric
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This paper studies smoothing parameter selection problem in nonparametric regression based on smoothing spline method for different data sets. For this aim, a Monte Carlo simulation study was performed. This simulation study provides a... more
This paper studies smoothing parameter selection problem in nonparametric regression based on smoothing spline method for different data sets. For this aim, a Monte Carlo simulation study was performed. This simulation study provides a comparison of the five popular selection criteria called as cross-validation (CV), generalized cross-validation (GCV), improved Akaike information criterion (AIC,), Mallows’ Cp and risk estimation using classical pilots (RCP). Empirical performances of five selection criteria were examined for this simulation and the most suitable one was selected accordingly.
This paper presents a comparative study of the hybrid models, neural networks and nonparametric regression models in time series forecasting. The components of these hybrid models are consisting of the nonparametric regression and... more
This paper presents a comparative study of the hybrid models, neural networks and nonparametric regression models in time series forecasting. The components of these hybrid models are consisting of the nonparametric regression and artificial neural networks models. Smoothing spline, regression spline and additive regression models are considered as the nonparametric regression components. Furthermore, various multilayer perceptron algorithms and radial basis function network model are regarded as the artificial neural networks components. The performances of these models are compared by forecasting the series of number of produced Cars and Domestic product per capita (GDP) data occurred in Turkey. This comparisons show that hybrid models proposed in this paper have denoted much more excellent performance than the hybrid models in literature.
Research Interests: Time Series, Radial Basis Function, Neural Networks, Neural Network, Time Series Prediction, and 9 moreKey words, Hybrid Models, Nonparametric Regression, Multilayer Perceptron, Radial Basis Function Neural Network, Time Series Forecasting, Regression Model, Artificial Neural Network, and Smoothing Spline
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Present study is about using of nonparametric models for GDP (Gross Domestic Product) per capita prediction in Turkey. It has been considered two alternative situations due to seasonal effects. In the first case, it is discussed a... more
Present study is about using of nonparametric models for GDP (Gross Domestic Product) per capita prediction in Turkey. It has been considered two alternative situations due to seasonal effects. In the first case, it is discussed a semi-parametric model where parametric component is dummy variable for the seasonality. In the second case, it is considered the seasonal component to be a smooth function of time, and therefore, the model falls within the class of additive models. The results obtained by semi-parametric regression models are compared to those obtained by additive nonparametric and parametric linear models. i s t denotes the seasonal component, ( ) i z t represents the trend, and ( ) i e t represents the terms of error with zero mean and common variance 2 e σ . The