Determining the dimension of iterative Hessian transformation

• 成果类型: Article
• 署名作者: Cook, RD; Bing, L
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000661
• 发表日期: 2004
• 页码: 2501-2531
• 关键词: sliced inverse regression; reduction; DIRECTIONS

摘要

The central mean subspace (CMS) and iterative Hessian transformation (IHT) have been introduced recently for dimension reduction when the conditional mean is of interest. Suppose that X is a vector-valued predictor and Y is a scalar response. The basic problem is to find a lower-dimensional predictor n(T)X such that E(Y\X) = E(Y\n(T)X). The CMS defines the inferential object for this problem and IHT provides an estimating procedure. Compared with other methods, IHT requires fewer assumptions and has been shown to perform well when the additional assumptions required by those methods fail. In this paper we give an asymptotic analysis of IHT and provide stepwise asymptotic hypothesis tests to determine the dimension of the CMS, as estimated by IHT. Here, the original IHT method has been modified to be invariant under location and scale transformations. To provide empirical support for our asymptotic results, we will present a series of simulation studies. These agree well with the theory. The method is applied to analyze an ozone data set.