Model Selection for Exponential Power Mixture Regression Models.

Area of Science:

• Statistics
• Machine Learning

Background:

• Finite mixture of linear regression (FMLR) models are essential for analyzing heterogeneous data.
• Existing methods may not efficiently handle simultaneous component number determination and variable selection.

Purpose of the Study:

• To develop a novel procedure for FMLR models that simultaneously determines the number of components and performs variable selection.
• To utilize an exponential power error distribution, encompassing normal and Laplace distributions, for enhanced model flexibility.

Main Methods:

• Introduced a new procedure for FMLR models incorporating an exponential power error distribution.
• Established theoretical consistency for order and variable selection under regularity conditions.
• Investigated asymptotic normality for non-zero parameter estimators.
• Proposed efficient modified expectation-maximization (EM) and majorization-maximization (MM) algorithms for optimization.

Main Results:

• The proposed method demonstrated consistency in both order and variable selection.
• Asymptotic normality was established for parameter estimators.
• Numerical simulations confirmed the finite sample performance of the methodology.
• Application to baseball salary data yielded a smaller Bayesian Information Criterion (BIC) value compared to existing methods.

Conclusions:

• The developed procedure effectively addresses simultaneous component number determination and variable selection in FMLR models.
• The use of exponential power error distribution offers a flexible framework for modeling heterogeneous data.
• The proposed algorithms provide efficient implementation for the statistical problem.