Meta-analysis, pretest, and shrinkage estimation of kurtosis parameters

ABSTRACT

An asymptotic theory for the improved estimation of kurtosis parameter vector is developed for multi-sample case using uncertain prior information (UPI) that several kurtosis parameters are the same. Meta-analysis is performed to obtain pooled estimator, as it is a statistical methodology for pooling quantitative evidence. Pooled estimator is a good choice when assumption of homogeneity holds but it becomes inconsistent as assumption violates, therefore pretest and Stein-type shrinkage estimators are proposed as they combine sample and nonsample information in a superior way. Asymptotic properties of suggested estimators are discussed and their risk comparisons are also mentioned.

KEYWORDS:

• Asymptotic distributional bias
• Asymptotic quadratic risk
• Kurtosis
• Meta-Analysis
• Shrinkage and pretest estimation
• Simulation
• Uncertain prior information

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F12
• 62P20
• 62H12

Acknowledgment

Thanks are also due to the editor and referees for their valuable output that improved this article.

Funding

The authors gratefully acknowledge the financial support provided by Thammasat University under the TU Research Scholar, Contract No. 50/2559.