Testing approximate normality of an estimator using the estimated MSE and bias with an application to the shape parameter of the generalized Pareto distribution

TL;DR

This paper proposes a method to test the normality of estimators using estimated MSE and bias, facilitating hypothesis testing in small samples, with an application to the shape parameter of the generalized Pareto distribution.

Contribution

It introduces a novel procedure for testing estimator normality based on estimated MSE and bias, aiding in model selection and hypothesis testing.

Findings

A new normality test for estimators using MSE and bias.

Application to estimate confidence intervals for the S&P 500 index.

Demonstrates effectiveness in small sample scenarios.

Abstract

Often it is not easy to choose between estimators, based on the estimated MSE and bias using simulation studies. Normality in small samples and a variance of the estimator, which is correct and easy to calculate using a single sample, give the added advantage that hypotheses concerning the parameter can be tested in new samples. A procedure to check normality is proposed where previously published MSE and bias are used to perform a test for normality. A confidence interval for the index of the S&P500 index is found by applying the results to estimators of the generalized Pareto distribution.