截尾平均數

Abstract

我們介紹一種新的截尾平均數，稱為眾數截尾平均數。衡量估計量穩健與否，破壞點是一個重要的準則，目前被提出的穩健估計量中，破壞點皆小於或等於0.5，我們將證明眾數截尾平均數的破壞點可以趨近於1。藉由模擬比較傳統截尾平均數和眾數截尾平均數的均方差。更進一步介紹及探討由眾數截尾平均數延伸建構出的一種新的 Winsorized 平均數。

We introduce a new type of trimmed mean, called the mode type trimmed mean. With the fact that the breakdown point is one important criterion for measuring the robust type estimators and the fact that the proposed robust estimators are all with breakdown points less than or equal to 0.5(see this point in Hampel et al. (1986)),we will show that this new trimmed mean may have breakdown point as large as close to 1. Simulation for comparing this trimmed mean and the traditional one will also be conducted through the mean square error (MSE). Moreover, an extension of this new type of trimmed mean to construct a new Winsorized mean will also be introduced and studied.