Model Selection for Exponential Power Mixture Regression Models

Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for...

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Published in:Entropy (Basel, Switzerland) Vol. 26; no. 5; p. 422
Main Authors: Jiang, Yunlu, Liu, Jiangchuan, Zou, Hang, Huang, Xiaowen
Format: Journal Article
Language:English
Published: Switzerland MDPI AG 01.05.2024
Subjects:
Algorithms
Approximation
Consistency
exponential power distribution
Feature selection
finite mixture of linear regression models
Lagrange multiplier
Maximization
Mixtures
modified EM algorithm
Normality
Numerical analysis
Optimization
Parameter modification
Regression models
Simulation methods
Sparsity
Statistical analysis
variable selection
Variables
Iran
exponential power distribution
finite mixture of linear regression models
variable selection
modified EM algorithm
ISSN:1099-4300, 1099-4300
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Abstract Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method.
AbstractList Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method.
Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method.Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method.
Audience Academic
Author Liu, Jiangchuan
Huang, Xiaowen
Zou, Hang
Jiang, Yunlu
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BackLink https://www.ncbi.nlm.nih.gov/pubmed/38785671$$D View this record in MEDLINE/PubMed
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10.2307/2532881
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finite mixture of linear regression models
variable selection
modified EM algorithm
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SubjectTerms Algorithms
Approximation
Consistency
exponential power distribution
Feature selection
finite mixture of linear regression models
Lagrange multiplier
Maximization
Mixtures
modified EM algorithm
Normality
Numerical analysis
Optimization
Parameter modification
Regression models
Simulation methods
Sparsity
Statistical analysis
variable selection
Variables
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