Dr. Song-Show Cheng 鄭松壽

1968 B.S. Dept. Math., Tamkang College of Arts & Sciences
1970 M.S. Inst. Math., Natl. Tsing-Hua Univ.
1979 Ph. D. Dept. Math. Memphis State U.
1980- Assoc. Prof. Grad. Inst. of Stat., NCU

　

  

通常在均值分析模式，大多假設觀測值來自常態分析之母體。我們現在假設：k個樣本之母體分布為t型族分配群；此分配涵蓋多種分配，( 包括柯西及常態分配 ) 是對稱、單峰之位置 ― 尺度分配群。 

            對單一樣本問題，我們將基於使用漸近變異數極小之概念，找出一個對均值 的簡單L型估計。此估計有效性高，且可能比Tiku和Suresh (1992) 提出之修改最大概似估計來得穩健。對k個樣本問題，我們將用Tiku的修改最大概似估計到Brown和Forsyth (1974) 的統計量，找出對應假設k個均值皆相等的一個穩健檢定。同時，我們也考慮分別以無資訊的和穩健的事前分布，及利用修改最大概似估計，來做貝氏推論；即找出對位置和尺度參數之最大事後密估計，對位置參數之最大事後區間。關於兩個樣本問題，我們將探討兩個均值之差之貝氏推論。

　

　

Robust Procedures for the Analysis of Means 

     In the analysis of means model, it is usually assumed that the observations come from a normal distribution.  We suppose instead that the distributions of the k-samples belong to a t-type family of distributions, which has a wide range of distributions including the Cauchy distribution and the normal distribution.  The t-type distributions are a location-scale family of symmetric unimodal distributions.

     For the one-sample problem, we aim to find a simple L-estimator for the mean , based on minimizing the assymptotic variance, which may be efficient and more robust than the MML ( modified maximum likelihood ) estimator developed by Tiku and Suresh (1992).  For k-samples, we are developing a robust procedure for testing the hypothesis that all k means are equal by applying Tiku’s MML procedures of estimating the location and scale parameters to the Brown & Forsyth’s (1974) statistic.  We are  also considering the Bayesian approach using some non-informative priors and robust priors and utilizing the MML estimators to develop the HPD ( highest posterior density ) estimators for the location and scale parameters, and the HPD intervals for the location. For the two-sample problem, we are investigating the Bayesian inference regarding the difference of two means.

　

　

Recent Publications:

 1.    Cheng, S. S. and Chen, B. R. (1991). The Locally MIMSQE of Nonnormal Error Variance in Quadratically Balanced Models. Metrika 38, 67-70.

 2.        Cheng, S. S. and Cheng, Y. C. (1998). An ordered relation between the ANOVA estimator of the interclass correlation and a kappa-type statistic in a binary data. Statistics & Probability Letters 38, 275-280.