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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References listed on IDEAS
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- Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
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- Liping Zhu & Tao Wang & Lixing Zhu & Louis Ferré, 2010. "Sufficient dimension reduction through discretization-expectation estimation," Biometrika, Biometrika Trust, vol. 97(2), pages 295-304.
- Bentler, Peter M. & Xie, Jun, 2000. "Corrections to test statistics in principal Hessian directions," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 381-389, May.
- 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.
- Prasad A. Naik & Chih-Ling Tsai, 2005. "Constrained Inverse Regression for Incorporating Prior Information," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 204-211, March.
- Cook, R. Dennis & Ni, Liqiang, 2005. "Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 410-428, June.
- Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
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