Robust parameter estimation based on the generalized log-likelihood in the context of Sharma-Taneja-Mittal measure

Area of Science:

• Statistical physics
• Information theory
• Geophysics
• Statistical inference

Background:

• Estimating unmeasurable physical parameters from observed data is crucial in science.
• Maximum likelihood estimation with Gaussian distributions is a common but sensitive method, failing with outliers.
• Outliers violate the Gauss-Markov theorem, rendering traditional methods ineffective.

Purpose of the Study:

• To develop an outlier-resistant approach for estimating physical parameters from noisy data.
• To propose a generalized log-likelihood estimation method based on the Sharma-Taneja-Mittal (STM) information measure.
• To address the limitations of traditional Gaussian-based methods in the presence of outliers.

Main Methods:

• Utilized a generalized logarithmic function associated with the Sharma-Taneja-Mittal (STM) information measure.
• Developed a generalized log-likelihood estimation technique.
• Deformed the Gaussian distribution using a two-parameter generalization of the logarithmic function.
• Tested the method on a geophysical inverse problem with a noisy dataset.

Main Results:

• The proposed STM-based generalized log-likelihood estimation demonstrated superior performance in estimating physical parameters from noisy data with outliers.
• The method effectively handled spurious observations that would invalidate traditional Gaussian-based approaches.
• Outperformed the classic maximum likelihood estimation in the tested geophysical inverse problem.

Conclusions:

• The proposed outlier-resistant method is a valuable tool for statistical physics, information theory, and statistical inference.
• It offers a robust alternative to traditional methods when dealing with datasets containing outliers.
• The generalized log-likelihood estimation based on the STM measure provides more reliable parameter estimation in challenging data conditions.