Heavy or semi-heavy tail, that is the question

Area of Science:

• Statistics
• Probability Theory
• Econometrics

Background:

• Traditional extreme value analysis often relies on heavy-tailed distributions.
• However, data exhibiting semi-heavy tails with a few outliers are common but less understood.
• Existing models may not adequately capture these specific data characteristics.

Purpose of the Study:

• To introduce novel skewed distribution families based on the hyperbolic secant distribution.
• To extend the concept of semi-heavy-tailedness to linear regression models.
• To investigate the properties of Maximum Likelihood (ML) estimators for regression parameters under semi-heavy-tailed error distributions.

Main Methods:

• Development of two new skewed distribution families.
• Extension of semi-heavy-tailed properties to a linear regression framework.
• Asymptotic analysis of ML estimators for regression parameters.
• Simulation studies comparing ML estimators under different error distributions.
• Application to three real-world datasets.

Main Results:

• The proposed skewed distributions exhibit desirable properties for modeling semi-heavy-tailed data.
• The study provides theoretical insights into the asymptotic behavior of ML estimators in semi-heavy-tailed regression.
• Simulation results demonstrate the effectiveness of the proposed methods.
• Real-world examples highlight the superiority of semi-heavy-tailedness over heavy-tailedness in specific contexts.

Conclusions:

• The new skewed hyperbolic secant distributions offer a valuable tool for analyzing data with semi-heavy tails.
• The proposed regression framework enhances parameter estimation accuracy when dealing with such data.
• The findings suggest that considering semi-heavy-tailedness is crucial for robust statistical modeling in the presence of limited outliers.