The Robust EM-type Algorithms for Log-concave Mixtures of Regression Models

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Finite mixture of regression (FMR) models are powerful tools for modeling data with unobserved heterogeneity.
• Traditional FMR models often rely on strong parametric assumptions, such as normally distributed residuals, which can lead to biased estimations if misspecified.
• The expectation-maximization (EM) algorithm is a common method for estimating FMR models but is sensitive to distributional assumptions.

Purpose of the Study:

• To develop novel estimation methods for FMR models that relax the strict parametric assumptions on component error densities.
• To propose EM-type algorithms that only assume log-concave error densities, allowing for greater flexibility.
• To compare the performance of these new methods against standard normal mixture EM algorithms.

Main Methods:

• Reformulation of FMR models as incomplete data problems.
• Development of two EM-type algorithms tailored for mixtures of regression models with log-concave error densities.
• Numerical studies to evaluate the performance and robustness of the proposed algorithms.

Main Results:

• The proposed methods demonstrate significantly smaller mean squared errors (MSEs) compared to standard normal mixture EM algorithms when component error densities deviate from normality.
• When the underlying component error densities are indeed normal, the new methods exhibit performance comparable to the traditional normal EM algorithm.
• The algorithms effectively handle FMR models without requiring specific parametric forms for component error distributions.

Conclusions:

• The proposed EM-type algorithms offer a more robust and flexible approach to estimating FMR models, particularly when distributional assumptions are uncertain.
• These methods provide a valuable alternative to standard techniques, leading to more reliable parameter estimates in a wider range of applications.
• The findings highlight the benefits of relaxing parametric assumptions in mixture regression modeling.