New Approaches to Model-free Dimension Reduction for Bivariate Regression
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.
X. M. Wen and R. D. Cook, "New Approaches to Model-free Dimension Reduction for Bivariate Regression," Journal of Statistical Planning and Inference, Elsevier, Mar 2009.
The definitive version is available at https://doi.org/10.1016/j.jspi.2008.01.017
Mathematics and Statistics
National Science Foundation (U.S.)
Keywords and Phrases
bivariate dimension reduction; censoring regression; central subspaces; intra-slice information; testing predictor effects
Article - Journal
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