On Model-Free Conditional Coordinate Tests For Regressions
de Leeuw, J.
Existing model-free tests of the conditional coordinate hypothesis in sufficient dimension reduction (Cook (1998) ) focused mainly on the first-order estimation methods such as the sliced inverse regression estimation (Li (1991) ). Such testing procedures based on quadratic inference functions are difficult to be extended to second-order sufficient dimension reduction methods such as the sliced average variance estimation (Cook and Weisberg (1991) ). In this article, we develop two new model-free tests of the conditional predictor hypothesis. Moreover, our proposed test statistics can be adapted to commonly used sufficient dimension reduction methods of eigendecomposition type. We derive the asymptotic null distributions of the two test statistics and conduct simulation studies to examine the performances of the tests.
Z. Yu et al., "On Model-Free Conditional Coordinate Tests For Regressions," Journal of Multivariate Analysis, Elsevier, Jan 2012.
The definitive version is available at http://dx.doi.org/10.1016/j.jmva.2012.02.004
Mathematics and Statistics
Keywords and Phrases
Conditional Coordinate Test; Sufficient Dimension Reduction; Sliced Inverse Regression
Article - Journal
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