Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.... more Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.We show, using a Monte Carlo study, that MM-estimates with projec- tion estimates as starting point of an iterative weighted least squares algorithm, behave more robustly than MM-estimates starting at an S-estimate and similar Gaussian efficiency. Moreover the former have a robustness behavior close to the P-estimates with an additional advantage: they are asymptotically normal making statistical inference possible
We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach ... more We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper definition of local symmetry is given. Moreover, strong consistency results for the local depth and also for the local depth regions are attained. Finally, applications to descriptive data analysis and classification are analyzed, making the special focus on multivariate functional data, where we obtain very promising results.
This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The c... more This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap statistic that provides local information to identify the instant with more clustering evidence in trajectories or derivatives. Then functional boxplots allow reconsidering overall allocation and each observation is finally assigned to the cluster where it spends most of the time within whiskers. These local and global searches are repeated recursively until there is no evidence of clustering at any time on trajectories or first and second derivatives. SeqClusFD simultaneously estimates the number of groups and provides data allocation. It also provides valuable information about the most important features that determine cluster structure. Computational aspects have been analyzed and the new method is tested on synthetic and real data sets.
In this paper we tackle the problems of dimensionality of welfare and that of iden-tifying the mu... more In this paper we tackle the problems of dimensionality of welfare and that of iden-tifying the multidimensionally poor by first finding the poor using the original space of attributes, and then reducing the welfare space. The starting point is the notion that the ‘poor ’ constitutes a group of individuals that are essentially different from the ‘non-poor ’ in a truly multidimensional framwework. Once this group has been iden-tified, we propose reducing the dimension of the original welfare space by solving the problem of finding the smallest set of attributes that can reproduce as accurately as possible the ‘poor/non-poor ’ classification in the first stage.
We herein introduce a general local depth measure for data in a Banach space, based on the use of... more We herein introduce a general local depth measure for data in a Banach space, based on the use of one-dimensional projections. Theoretical properties of the local depth measure are studied, as well as, strong consistency results of the local depth measure and also of the local depth regions. In addition, we propose a clustering procedure based on local depths. Applications of the clustering procedure are illustrated on some artificial and real data sets for multivariate, functional and multifunctional data, obtaining very promising results.
In this article we introduce two procedures for variable selection in cluster analysis and classi... more In this article we introduce two procedures for variable selection in cluster analysis and classification rules. One is mainly aimed at detecting the “noisy ” noninformative variables, while the other also deals with multicolinearity and general dependence. Both methods are designed to be used after a “satisfactory ” grouping procedure has been carried out. A forward–backward algorithm is proposed to make such procedures feasible in large datasets. A small simulation is performed and some real data examples are analyzed.
This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The c... more This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap statistic that provides local information to identify the instant with more clustering evidence in trajectories or derivatives. Then functional boxplots allow reconsidering overall allocation and each observation is finally assigned to the cluster where it spends most of the time within whiskers. These local and global searches are repeated recursively until there is no evidence of clustering at any time on trajectories or first and second derivatives. SeqClusFD simultaneously estimates the number of groups and provides data allocation. It also provides valuable information about the most important features that determine cluster structure. Computational aspects have been analyzed and the new method is tested on synthetic and real data sets.
We herein introduce a general local depth measure for data in a Banach space, based on the use of... more We herein introduce a general local depth measure for data in a Banach space, based on the use of one-dimensional projections. Theoretical properties of the local depth measure are studied, as well as, strong consistency results of the local depth measure and also of the local depth regions. In addition, we propose a clustering procedure based on local depths. Applications of the clustering procedure are illustrated on some artificial and real data sets for multivariate, functional and multifunctional data, obtaining very promising results.
Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.... more Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.We show, using a Monte Carlo study, that MM-estimates with projec- tion estimates as starting point of an iterative weighted least squares algorithm, behave more robustly than MM-estimates starting at an S-estimate and similar Gaussian efficiency. Moreover the former have a robustness behavior close to the P-estimates with an additional advantage: they are asymptotically normal making statistical inference possible
We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach ... more We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper definition of local symmetry is given. Moreover, strong consistency results for the local depth and also for the local depth regions are attained. Finally, applications to descriptive data analysis and classification are analyzed, making the special focus on multivariate functional data, where we obtain very promising results.
This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The c... more This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap statistic that provides local information to identify the instant with more clustering evidence in trajectories or derivatives. Then functional boxplots allow reconsidering overall allocation and each observation is finally assigned to the cluster where it spends most of the time within whiskers. These local and global searches are repeated recursively until there is no evidence of clustering at any time on trajectories or first and second derivatives. SeqClusFD simultaneously estimates the number of groups and provides data allocation. It also provides valuable information about the most important features that determine cluster structure. Computational aspects have been analyzed and the new method is tested on synthetic and real data sets.
In this paper we tackle the problems of dimensionality of welfare and that of iden-tifying the mu... more In this paper we tackle the problems of dimensionality of welfare and that of iden-tifying the multidimensionally poor by first finding the poor using the original space of attributes, and then reducing the welfare space. The starting point is the notion that the ‘poor ’ constitutes a group of individuals that are essentially different from the ‘non-poor ’ in a truly multidimensional framwework. Once this group has been iden-tified, we propose reducing the dimension of the original welfare space by solving the problem of finding the smallest set of attributes that can reproduce as accurately as possible the ‘poor/non-poor ’ classification in the first stage.
We herein introduce a general local depth measure for data in a Banach space, based on the use of... more We herein introduce a general local depth measure for data in a Banach space, based on the use of one-dimensional projections. Theoretical properties of the local depth measure are studied, as well as, strong consistency results of the local depth measure and also of the local depth regions. In addition, we propose a clustering procedure based on local depths. Applications of the clustering procedure are illustrated on some artificial and real data sets for multivariate, functional and multifunctional data, obtaining very promising results.
In this article we introduce two procedures for variable selection in cluster analysis and classi... more In this article we introduce two procedures for variable selection in cluster analysis and classification rules. One is mainly aimed at detecting the “noisy ” noninformative variables, while the other also deals with multicolinearity and general dependence. Both methods are designed to be used after a “satisfactory ” grouping procedure has been carried out. A forward–backward algorithm is proposed to make such procedures feasible in large datasets. A small simulation is performed and some real data examples are analyzed.
This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The c... more This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap statistic that provides local information to identify the instant with more clustering evidence in trajectories or derivatives. Then functional boxplots allow reconsidering overall allocation and each observation is finally assigned to the cluster where it spends most of the time within whiskers. These local and global searches are repeated recursively until there is no evidence of clustering at any time on trajectories or first and second derivatives. SeqClusFD simultaneously estimates the number of groups and provides data allocation. It also provides valuable information about the most important features that determine cluster structure. Computational aspects have been analyzed and the new method is tested on synthetic and real data sets.
We herein introduce a general local depth measure for data in a Banach space, based on the use of... more We herein introduce a general local depth measure for data in a Banach space, based on the use of one-dimensional projections. Theoretical properties of the local depth measure are studied, as well as, strong consistency results of the local depth measure and also of the local depth regions. In addition, we propose a clustering procedure based on local depths. Applications of the clustering procedure are illustrated on some artificial and real data sets for multivariate, functional and multifunctional data, obtaining very promising results.
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