Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter

Abstract

In this paper, the inference on location parameter for the skew-normal population is considered when the scale parameter and skewness parameter are unknown. Firstly, the Bootstrap test statistics and Bootstrap confidence intervals for location parameter of single population are constructed based on the methods of moment estimation and maximum likelihood estimation, respectively. Secondly, the Behrens-Fisher type and interval estimation problems of two skew-normal populations are discussed. Thirdly, by the Monte Carlo simulation, the proposed Bootstrap approaches provide the satisfactory performances under the senses of Type I error probability and power in most cases regardless of the moment estimator or ML estimator. Further, the Bootstrap test based on the moment estimator is better than that based on the ML estimator in most situations. Finally, the above approaches are applied to the real data examples of leaf area index, carbon fibers’ strength and red blood cell count in athletes to verify the reasonableness and effectiveness of the proposed approaches.

Investigating the Effect of Small Sample Process Capability Index Under Different Bootstrap Methods

“…The core idea of Bootstrap method is to replace theoretical analysis with computer simulation technology, that is, to extract the same number of samples from the original samples by repeated sampling technology, and replace the real distribution with its statistics. Bootstrap method can be used for the hypothesis testing and interval estimation problems of location parameter with unknown scale parameter and skewness parameter, it provides the satisfactory performances under the senses of Type I error probability and power in most cases regardless of the moment estimator or ML estimator [9]. By repeating the above process and calculating its mean or variance, the empirical distribution of statistics is substituted for the real distribution.…”