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

Hao Hu1, Weixin Yao2, Yichao Wu1

  • 1Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.

Computational Statistics & Data Analysis
|September 27, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces new methods for finite mixture of regression (FMR) models, relaxing assumptions about error distributions. The novel algorithms offer improved accuracy when component error densities are non-normal, demonstrating reduced mean squared errors (MSEs).

Keywords:
EM algorithmLog-concave Maximum Likelihood EstimatorMixture of Regression ModelRobust regression

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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.