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http://dx.doi.org/10.5351/KJAS.2005.18.2.381

Asymptotic Test for Dimensionality in Sliced Inverse Regression  

Park, Chang-Sun (Department of Statistics, Sungkyunkwan University)
Kwak, Jae-Guen (Department of Statistics, Sungkyunkwan University)
Publication Information
The Korean Journal of Applied Statistics / v.18, no.2, 2005 , pp. 381-393 More about this Journal
Abstract
As a promising technique for dimension reduction in regression analysis, Sliced Inverse Regression (SIR) and an associated chi-square test for dimensionality were introduced by Li (1991). However, Li's test needs assumption of Normality for predictors and found to be heavily dependent on the number of slices. We will provide a unified asymptotic test for determining the dimensionality of the SIR model which is based on the probabilistic principal component analysis and free of normality assumption on predictors. Illustrative results with simulated and real examples will also be provided.
Keywords
Sliced inverse regression; Dimension reduction; Latent variable model; Asymptotic test;
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