平行多變量分位數區域

Abstract

在單維度下，分位數區間有許多的應用。但在多維度的情形下，儘管多維度的分位數已被提出(Chaudhuri (1996)、Chen and Welsh (1999))，如此的多維度分位數並不能適當地定義出分位數區間。我們提出以平行四邊形區域為多維度分位數區域，與區域為橢圓相較，討論在常態分配、指數分配和卡方分配下的有效性。我們並以平行四邊形區域發展一些應用，其中深入探討多維度修飾後平均數的大樣本性質以及其效率。

There are many applications of the quantile interval for statistical inference in univariate distribution. Under multivariate dimension, although the multivariate quantile has been proposed (Chaudhuri(1996)、Chen and Welsh(1999)), the use of their quantiles for constructing multivariate region is not satisfactory. We propose a multivariate quantile region in the form of a parallelogram. Comparing with ellipsoid, we discuss the validity of the multivariate quantile regions under normal, exponential, and chi-square distribution. We also develop some applications of this parallel region, and study the multivariate trimmed mean constructed based on this region advancedly for its large sample property and efficiency.