Determining the dimension of iterative Hessian transformation

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dc.creatorCook, R. Dennis
dc.creatorLi, Bing
dc.date2005-08-30
dc.date.accessioned2026-07-07T08:07:15Z
dc.date.available2026-07-07T08:07:15Z
dc.descriptionThe 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 η^TX such that E(Y|X)=E(Y|η^TX). 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053604000000661 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0508598
dc.identifierhttp://arxiv.org/abs/math/0508598
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 6, 2501-2531
dc.identifierdoi:10.1214/009053604000000661
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130879
dc.subjectStatistics Theory
dc.subject62G08 (Primary) 62G09, 62H05. (Secondary)
dc.titleDetermining the dimension of iterative Hessian transformation
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