Comparative Study on Probability Density Estimators of Sample Maximum and Data Transformation

Accepted - March 2024

Abstract

Comparative studies on estimators of the probability density function of sample maximum are conducted. This study presents a plug-in type of and a new block-maxima-based kernel density estimators as the alternatives of the parametric estimator fitting to the approximate generalized extreme value density function. Asymptotic properties of the density estimators are investigated, which shows that the optimal convergence rates depend on the extreme index of the distribution. Furthermore, this study investigates the density estimators with data log-transformation. It is demonstrated that the log-transformation makes the estimators numerically stable in finite sample case. Finally, two illustrative examples are provided.