與解釋變數相關群體平均的有母數與無母數統計推論

Abstract

分析群體平均數通常是由傳統的變異數分析來執行。但是在許多流行病學的 問題裡，分群牽涉到另外一個解釋變數。這類群體平均數被HAN(2006)證明， 傳統變異數分析所需的條件(常態及相同變異數等)均不成立。在分群所用的分割 點已知及未知情況下，我們考慮無母數及有母數群體平均的統計推論。在無母數 的群平均估計量我們將導出大樣本分配來建立信賴區間及檢定規則。在有母數方 法我們將假設常態分配。再經由分配參數的mle來估計群平均估計量。那mle 的大樣本性質就可導出群平均估計量的分配。統計推論性質也可推導出。另外我 們也將由無母數群平均估計建立一個穩健性估計之截斷平均數。這將是一個好的 穩健估計法。其有效性將被分析。

Group means are usually analyzed through the classical ANOVA methods. We propose and study a parametric and nonparametric inference methods for data when grouping is involved with an explanatory variable, occurred often in public health statistical problems. Under the nonparametric group mean estimator, we will derive its large sample distribution and use it to construct C.I. and test for hypothesis of group means. Under the parametric estimation, we will consider normal distribution that allows us to estimate the group means through the mle of distributional parameters. And the large sample property of mle allows us to construct C.I. and test based on parametric group mean estimator. We will also construct a trimmed mean estimator. Its large sample efficiency will be studied.