TY - JOUR
T1 - New approaches to model-free dimension reduction for bivariate regression
AU - Wen, Xuerong Meggie
AU - Cook, R. Dennis
PY - 2009/3/1
Y1 - 2009/3/1
N2 - Dimension reduction with bivariate responses, especially a mix of a continuous and categorical responses, can be of special interest. One immediate application is to regressions with censoring. In this paper, we propose two novel methods to reduce the dimension of the covariates of a bivariate regression via a model-free approach. Both methods enjoy a simple asymptotic chi-squared distribution for testing the dimension of the regression, and also allow us to test the contributions of the covariates easily without pre-specifying a parametric model. The new methods outperform the current one both in simulations and in analysis of a real data. The well-known PBC data are used to illustrate the application of our method to censored regression.
AB - Dimension reduction with bivariate responses, especially a mix of a continuous and categorical responses, can be of special interest. One immediate application is to regressions with censoring. In this paper, we propose two novel methods to reduce the dimension of the covariates of a bivariate regression via a model-free approach. Both methods enjoy a simple asymptotic chi-squared distribution for testing the dimension of the regression, and also allow us to test the contributions of the covariates easily without pre-specifying a parametric model. The new methods outperform the current one both in simulations and in analysis of a real data. The well-known PBC data are used to illustrate the application of our method to censored regression.
KW - Bivariate dimension reduction
KW - Censoring regression
KW - Central subspaces
KW - Intra-slice information
KW - Testing predictor effects
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U2 - 10.1016/j.jspi.2008.01.017
DO - 10.1016/j.jspi.2008.01.017
M3 - Article
AN - SCOPUS:56949095494
SN - 0378-3758
VL - 139
SP - 734
EP - 748
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 3
ER -