Please use this identifier to cite or link to this item: https://doi.org/10.1214/009053607000000352
Title: A constructive approach to the estimation of dimension reduction directions
Authors: Xia, Y. 
Keywords: Conditional density function
Convergence of algorithm
Double-kernel smoothing
Efficient dimension reduction
Root-n consistency
Issue Date: Dec-2007
Citation: Xia, Y. (2007-12). A constructive approach to the estimation of dimension reduction directions. Annals of Statistics 35 (6) : 2654-2690. ScholarBank@NUS Repository. https://doi.org/10.1214/009053607000000352
Abstract: In this paper we propose two new methods to estimate the dimensionreduction directions of the central subspace (CS) by constructing a regression model such that the directions are all captured in the regression mean. Compared with the inverse regression estimation methods [e.g., J. Amer. Statist. Assoc. 86 (1991) 328-332, J. Amer. Statist. Assoc. 86 (1991) 316-342, J. Amer. Statist. Assoc. 87 (1992) 1025-1039], the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable, and have better performance than the inverse regression estimation methods for finite samples. Compared with the direct regression estimation methods [e.g., J. Amer. Statist. Assoc. 84 (1989) 986-995, Ann. Statist. 29 (2001) 1537-1566, J. R. Stat. Soc. Ser. B Stat. Methodol. 64 (2002) 363-410], which can only estimate the directions of CS in the regression mean, the new methods can detect the directions of CS exhaustively. Consistency of the estimators and the convergence of corresponding algorithms are proved. © Institute of Mathematical Statistics, 2007.
Source Title: Annals of Statistics
URI: http://scholarbank.nus.edu.sg/handle/10635/104925
ISSN: 00905364
DOI: 10.1214/009053607000000352
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