Smoothing Spline

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.

Three-dimensional (3-D) snow analysis techniques provide comprehensive and accurate snow microstructure data. Nevertheless, there remains a requirement for less elaborate methods for snow characterization, as numerical snow models such as SNOWPACK are presently based on two-dimensional (2-D) grain analysis. We present a detailed assessment of various methods and shape descriptors used for snow characterization from digitized images. Dendricity, the ratio

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.

This paper presents a data reduction method for functional data. Starting with noisy or not noisy data, we first define a function f, called the “reference function”, as a cubic smoothing spline which is supposed to have the global form of the data. This reference function is then used to locate the knots of the final approximating spline by using

Recently, considerable interest has been shown in the connection between smoothing splines and a particular class of stochastic processes. Here the connection with an equivalent class of least squares problems is used to develop algorithms, and properties of the solution are examined. We give an estimate of the condition number of the solution process and compare this with an estimate for the condition number of the Reinsch algorithm in its conventional implementation.

An issue that often arises in such GIS applications as digital elevation modeling (DEM) is how to create a continuous surface using a limited number of point observations. In hydrological applications, such as estimating drainage areas, direction of water flow is easier to detect from a smooth DEM than from a grid created using standard interpolation programs. Another reason for continuous mapping is esthetic; like a picture, a map should be visually appealing, and for some GIS users this is more important than map accuracy. There are many methods for local smoothing. Spline algorithms are usually used to create a continuous map, because they minimize curvature of the surface. Geostatistical models are commonly used approaches to spatial prediction and mapping in many scientific disciplines, but classical kriging models produce noncontinuous surfaces when local neighborhood is used. This motivated us to develop a continuous version of kriging. We propose a modification of kriging th...

Abstract. In this paper the interpolation by G2 continuous Bézier spline curves Bn in IRd is outlined. Each segment of the spline curve interpolates r interior and two boundary points. The general approach is followed in detail for the case d= 3, n= 3, r= 1. For the single ...

Abstract: In this paper we formulate a least squares problem on a Riemannian manifold M , in order to generate smoothing spline curves fitting a given data set of points in M , q0, q1, . . . , qN , at given instants of time t0 < t1 < · · · < tN . Using tools from Riemannian geometry, we derive the Euler-Lagrange equations associated to this variational problem and prove that its solutions are Riemannian cubic polynomials defined at each interval [ti, ti+1[, i = 0, . . . , N − 1, and satisfying some smoothing constraints at the knot points ti. The geodesic that best fits the data, arises as a limiting process of the above. When M is replaced by the Euclidean space IR, the proposed problem has a unique solution which is a natural cubic spline given explicitly in terms of the data. We prove that, in this case, the straight line obtained from the limiting process is precisely the linear regression line associated to the data. Using tools from optimization on Riemannian manifold...

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

La presente investigacion se realizo en el laboratorio de agromapas digitales de la region Golfo-Centro del Instituto Nacional de Investigaciones Forestales, Agricolas y Pecuarias en 2007. Se utilizo informacion de la precipitacion pluvial historica del periodo 1961 a 2003 del mes de septiembre, registrada en 147 estaciones meteorologicas pertenecientes a la red de estaciones del Servicio Meteorologico Nacional ubicadas dentro de una region que comprende parte del barlovento y sotavento de Mexico. El objetivo fue realizar una comparacion de cuatro metodos de interpolacion: inverso de la distancia, kriging, co-kriging y thin plate smoothing spline, de datos puntuales de precipitacion pluvial en la region de sotavento y barlovento de la Republica Mexicana. La informacion fue analizada para detectar si existe en esta region una relacion de la precipitacion pluvial con las variables de elevacion, longitud y distancia al oceano. Se observo que la superficie generada con el metodo thin pl...

Pendekatan nonparametrik digunakan ketika bentuk fungsi data yang diperoleh tidak menunjukkan suatu pola hubungan yang mudah untuk digambarkan dengan fungsi tertentu. Bentuk fungsi yang tidak diketahui tersebut dapat diestimasi menggunakan metode smoothing spline . Smoothing spline mengestimasi fungsi regresi nonparametrik berdasarkan pada suatu persoalan optimasi, yaitu yang  meminimumkan JKG dengan pembatasan bahwa fungsi cukup halus. Ini disebut dengan Penalized Least Square Regression ( PLS ). Metode smoothing spline diaplikasikan untuk mengestimasi rata-rata lama sekolah berdasarkan jumlah penduduk miskin Jawa-Bali tahun 2012. Kemudian estimator smoothing spline yang diperoleh dibandingkan dengan model linier dan kuadratik. Dalam skripsi ini diperoleh estimator smoothing spline pada model regresi nonparametrik yang memberikan estimasi fungsi regresi yang paling baik dengan menggunakan MSE sebagai kriteria pemilihan model paling andal.

Geotechnical design depends on parameters got from field investigations. Therefore the devel- opment of subsoil models for assessing the behaviour of the subsoil has a strong influence on the reliability of geotechnical structures. The contribution deals with an adaptive improvement of soil models using geostatis- tical methods, demonstrated for a data set of a simplified practical example. Starting with subjective

A class of fully discrete schemes for the numerical simulation of solutions of the periodic initial-value problem for a class of generalized Korteweg-de Vries equations is analysed, implemented and tested. These schemes may have arbitrarily high order in both the spatial and the temporal variable, but at the same time they feature weak theoretical stability limitations. The spatial discretization is effected using smooth splines of quadratic or higher degree, while the temporal discretization is a multi-stage, implicit, Runge-Kutta method. A proof is presented showing convergence of the numerical approximations to the true solution of the initial-value problem in the limit of vanishing spatial and temporal discretization. In addition, a careful analysis of the efficiency of particular versions of our schemes is given. The information thus gleaned is used in the investigation of the instability of the solitary-wave solutions of a certain class of these equations.

Splines have been investigated as a basic tool of applied mathematics. First, the dynamics splines based on control theory were used in trajectory planning. Many researchers have studied some of the basic properties of splines from the viewpoint of optical control. We consider the method for generating smoothing splines using a control theoretic approach. Namely, we make generalized splines by solving an optimal control problem for linear systems. Then, we treat dependence on initial conditions. The important contribution in this paper is as follows: We introduce the new smoothing splines by optimizing not only over the control but also over the initial condition data.

In recent years, most studies in the field of technology and trade have focused on the critical importance of technological change in explaining international trade patterns. Technological innovation is not taking place in all countries and it does not spread to all countries at the same time, therefore technological distance would exist among countries.This paper has explained  the effect of technological distance on Iran’s trade relations, specifying a semi-parametric gravity model over 1995-2015. As expected, the estimation results of semi-parametric gravity model show that the effect of GDP on bilateral trade relations between Iran and each of the selected trading partners is positive and significant. The population of the exporter has negative impact while the importer’s population has positive effect on bilateral trade. Our empirical results indicate that the relationship between technological distance and bilateral trade is nonparametric, implying a general effect of technology on Iran’s bilateral trade relations. More clearly, in some ranges of the technological distance a negative effect appears on trade relations, while in other fractions of the relevant distance, the impact is positive, leading to an increase in bilateral trade relations between Iran and its trading partners.