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On the robustification of the z-test statistic
Ryeji Jeong(정례지),Seung Bin Son(손승빈),Hee Joo Lee(이희주),Haewon Kim(김해원) 대한산업공학회 2018 대한산업공학회 춘계학술대회논문집 Vol.2018 No.4
The z-test statistic is one of the most popular statistics. However, this conventional z-test has a serious pitfall when some of observations in a sample are contaminated. We propose two alternatives which satisfy asymptotic normality. We used the median or Hodges-Lehmann estimator instead of the mean and we also used the median absolute deviation or Shamos estimator instead of the standard deviation in the z-test statistic. The proposed alternatives are easy to implement. Thus, it is quite useful for engineers and practitioners. Through extensive Monte Carlo simulations, we obtained the empirical statistical power curves which clearly show that the proposed alternatives outperform the traditional method based on the z-test. A real-data illustration is also provided.
On the robustification of the z-test statistic
Ryeji Jeong(정례지),Seung Bin Son(손승빈),Hee Joo Lee(이희주),Haewon Kim(김해원) 한국경영과학회 2018 한국경영과학회 학술대회논문집 Vol.2018 No.04
The z-test statistic is one of the most popular statistics. However, this conventional z-test has a serious pitfall when some of observations in a sample are contaminated. We propose two alternatives which satisfy asymptotic normality. We used the median or Hodges-Lehmann estimator instead of the mean and we also used the median absolute deviation or Shamos estimator instead of the standard deviation in the z-test statistic. The proposed alternatives are easy to implement. Thus, it is quite useful for engineers and practitioners. Through extensive Monte Carlo simulations, we obtained the empirical statistical power curves which clearly show that the proposed alternatives outperform the traditional method based on the z-test. A real-data illustration is also provided.