On model-free conditional coordinate tests for regressions
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.
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Volume (Year): 109 (2012)
Issue (Month): C ()
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- R. Dennis Cook & Liqiang Ni, 2006. "Using intraslice covariances for improved estimation of the central subspace in regression," Biometrika, Biometrika Trust, vol. 93(1), pages 65-74, March.
- Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
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