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

Author

Listed:
  • Rendao Ye

    (School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Bingni Fang

    (School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Weixiao Du

    (School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Kun Luo

    (Alibaba Business College, Hangzhou Normal University, Hangzhou 310036, China)

  • Yiting Lu

    (School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China)

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.

Suggested Citation

  • Rendao Ye & Bingni Fang & Weixiao Du & Kun Luo & Yiting Lu, 2022. "Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter," Mathematics, MDPI, vol. 10(6), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:921-:d:770264
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    References listed on IDEAS

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