Mathematics > Statistics Theory
[Submitted on 21 Mar 2014]
Title:On efficient dimension reduction with respect to a statistical functional of interest
View PDFAbstract:We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals: the linear functional, the composite linear functional and the implicit functional. In conjunction with our theoretical analysis, we also propose a class of one-step Newton-Raphson estimators and show by simulations that they substantially outperform existing methods. Finally, we apply the new method to construct the central mean and central variance subspaces for a data set involving the physical measurements and age of abalones, which exhibits a strong pattern of heteroscedasticity.
Submission history
From: Wei Luo [view email] [via VTEX proxy][v1] Fri, 21 Mar 2014 14:59:05 UTC (413 KB)
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