Information-Theoretic Aspects of Location Parameter Estimation under Skew-Normal Settings.

Area of Science:

• Statistics
• Probability Theory
• Asymmetric Data Modeling

Background:

• Normality assumption is frequently violated in real-world data, leading to skewed distributions.
• Skewness significantly impacts the accuracy of mean estimation.
• Skew-normal distributions offer a flexible framework for modeling asymmetric data.

Purpose of the Study:

• To compare two methods for estimating the location parameter (μ) in skew-normal distributions.
• To analyze the properties of the least square estimator (LSE) and the best unbiased estimator (BUE).
• To explore information-theoretic inequalities for quantifying estimation uncertainty.

Main Methods:

• Utilized skew-normal distribution theory.
• Investigated least square estimation (LSE) and best unbiased estimation (BUE) for the location parameter (μ).
• Applied information theory, including differential entropy and Fisher information, with convexity-based inequalities.

Main Results:

• Demonstrated that the best unbiased estimator (BUE) dominates the least square estimator (LSE) for μ in skew-normal settings.
• Derived lower and upper bounds for differential entropy and Fisher information.
• Simulations illustrated the behavior of these bounds.

Conclusions:

• The best unbiased estimator (BUE) provides a more accurate estimation of the location parameter (μ) in skewed data compared to LSE.
• Information-theoretic bounds offer a robust method for measuring the uncertainty in location parameter estimations.
• The study contributes to robust statistical modeling for asymmetric data.