巴式漸近相對有效性蒙地卡羅運算法

Computing Bahadur Asymptotic Relative Efficiency Using Monte Carlo Method

李泰明(Tai-Ming Lee)

《Journal of Data Analysis》 8卷1期 (2013/02) Pp. 69-83

https://doi.org/10.6338/JDA.201302_8(1).0005

摘要

漸近相對有效性的界定，提供了兩種立意相同的檢定法，有合理的比較基礎。當然界定可以有不同的方式，繼Pitman and Noether（1955）之後，最有名的就是Bahahur（1967）所界定的漸近相對有效性。巴式的漸近相對有效性，是將顯著水準趨向零，以使樣本數放大，而形成比值的極限。這樣的定義雖然完美，但在運算上卻是困難重重。Bahahur（1967）自己有提出一些近似的解法，都需相當繁複的數理推演。而本文是直接運用蒙地卡羅樣本去做檢定，再利用非線性迴歸，估計出期望P值函數。反推成樣本需求函數，進一步獲得樣本數的比值函數，並延伸成其極限值的解。這樣的方法稱之為蒙地卡羅最小平方和法。

關鍵字

巴式漸近相對有效性 ； 蒙地卡羅最小平方和法 ； 非線性迴歸

並列摘要

Asymptotic Relative Efficiency, constructed completely by Pitman (1948), is a useful concept in comparing different testing procedure with the same statistics goal. On the other hand, it is difficult to compute the ARE in general, since the power function should be approximated and inverted to obtain sample size requirement. A famers special case computed by Hodgens and Lehmann (1956) showed that the ARE is at least 0.864 in comparing Wilcoxon sum of rank and two sample t test.On this paper, the ARE defined by Bahadur (1967) are also studied. We propose the Monte Carlo Least Square method to estimate the power function, with which it is easy to invert the function. This general methodology can compute ARE with any specific population to compare different procedure. Several cases will be shown graphically and numerically.

並列關鍵字

Asymptotic Relative Efficiency ； Monte Carlo L.S. ； Logistic Regression

參考文獻

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