The Robustness of Confidence Intervals for Normal Mean Against Skew Normality

偏斜常態分佈架構下，常態平均值之信賴區間的穩健性探討

曾玉玲(Yu-Ling Tseng)；廖芊帙(Chien-Chih Liao)

穩健性 ； 信賴區間 ； 常態平均值 ； 偏斜常態 ； Confidence intervals ； Skew-normal distribution ； Robustness

中國統計學報

51卷4期（2013 / 12 / 01）

445 - 466

英文

常態分佈下平均值的信賴區間是統計分析中廣為應用的推論方法。許多文獻都探討資料偏離常態分佈假設時，統計推論的穩健性。本研究從偏斜常態分佈的架構下，探討常態平均值之信賴區間的穩健性。綜合理論推導及模擬的結果，得知常態分佈假設下之單邊或雙邊信賴區間的涵蓋機率會偏離其所宣稱的信賴係數，而偏離程度則會隨著偏斜參數越大或是樣本數越小而越嚴重。因此，在偏斜常態分佈的架構下，常態平均值之單邊及雙邊信賴區間在維持其信賴係數的表現不夠穩健。

The confidence intervals of a normal mean are widely used in statistical analyses. Various robustness against the departure of normality has been considered in the literature. This paper considers the robustness of confidence intervals of a normal mean under the skew-normality. Based on theoretical derivations and the results of a simulation study, we find that the coverage probabilities of the confidence intervals can be more seriously different from the nominal confidence coefficients for larger skew parameter or for smaller sample size. Therefore, the intervals would not be robust on maintaining their confidence coefficients when the skewness of the true shew-normality distribute is large.

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