Component selection for exponential power mixture models

Area of Science:

• Statistics
• Probability Theory
• Data Science

Background:

• The Exponential Power (EP) distribution family offers greater flexibility than the Gaussian family.
• Existing mixture models often assume zero component means, limiting their applicability.
• Robust statistical modeling requires flexible distributions and accurate component selection.

Purpose of the Study:

• To develop a method for simultaneous component selection and parameter estimation in EP mixture models and regressions.
• To relax the restrictive assumption of zero component means in prior work.
• To enhance the accuracy of statistical modeling for complex data.

Main Methods:

• A penalized likelihood approach is proposed to shrink mixing proportions, enabling automatic component selection.
• Modified Expectation-Maximization (EM) algorithms are developed for parameter estimation.
• The consistency of the estimated number of components is theoretically established.

Main Results:

• The penalized likelihood method effectively selects components by shrinking mixing proportions to zero.
• Modified EM algorithms provide accurate parameter and density estimations.
• Simulation studies demonstrate superior performance in component number selection and estimation accuracy compared to existing methods.

Conclusions:

• The proposed penalized likelihood method offers a robust and accurate approach for EP mixture models and regressions.
• The relaxation of the zero component mean assumption broadens the applicability of these models.
• The methods are validated through simulations and real-world data analyses, including financial risk and climate change.