Variable selection in finite mixture of regression models using the skew-normal distribution.

Area of Science:

• Statistics
• Statistical Modeling
• Regression Analysis

Background:

• Variable selection is crucial in finite mixture of regression (FMR) models.
• Standard FMR models often assume normal error distributions, which are inadequate for asymmetric data.
• Existing methods lack robustness when dealing with heterogeneous data exhibiting skewness.

Purpose of the Study:

• To develop a robust variable selection procedure for FMR models accommodating asymmetric error distributions.
• To introduce the use of the skew-normal distribution within the FMR framework for enhanced modeling flexibility.
• To establish the theoretical consistency and oracle properties of the proposed variable selection method.

Main Methods:

• Implementation of a variable selection procedure for FMR models utilizing the skew-normal distribution.
• Development of a modified Expectation-Maximization (EM) algorithm for parameter estimation in the skew-normal FMR models.
• Theoretical analysis to establish consistency in variable selection and the oracle property in estimation.

Main Results:

• The proposed method demonstrates consistency in variable selection, accurately identifying relevant predictors.
• The procedure achieves the oracle property in estimation, indicating efficient parameter estimation.
• Numerical experiments and a real data example validate the effectiveness of the skew-normal FMR approach.

Conclusions:

• The skew-normal distribution provides a flexible and effective alternative for variable selection in FMR models with asymmetric data.
• The developed methodology offers improved statistical modeling capabilities for complex datasets.
• The theoretical properties and empirical validation support the practical utility of this advanced statistical technique.