An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model

References

• Bellman, R. (1961), Adaptive Control Process: A Guide Tour, Princeton, NJ: Princeton.
   Google Scholar
• Bickel, P. J., Klaassen, C. A. J., Ritov, Y., and Wellner, J. A. (1998), Efficient and Adaptive Estimation for Semiparametric Models, New York: Springer.
   Google Scholar
• Bierens, H. J., and Hartog, J. (1988), “Nonlinear Regression With Discrete Explanatory Variables, With an Application to the Earnings Function,” Journal of Econometrics, 38, 269–299.
   Web of Science ®Google Scholar
• Borisenko, A. A., and Nikolaevskiĭ, Y. A. (1991), “Grassmann Manifolds and Grassmann Image of Submanifolds,” Uspekhi Matematicheskikh Nauk, 46, 41–83, 240.
   Google Scholar
• Breiman, L., and Friedman, J. H. (1985), “Estimating Optimal Transformations for Multiple Regression and Correlation,” Journal of the American Statistical Association, 80, 580–619.
   Web of Science ®Google Scholar
• Chiang, C. T., and Huang, M. Y. (2012), “New Estimation and Inference Procedures for a Single-Index Conditional Distribution Model,” Journal of Multivariate Analysis, 111, 271–285.
   Web of Science ®Google Scholar
• Chiaromonte, F., Cook, R. D., and Li, B. (2002), “Sufficient Dimension Reduction in Regression With Categorical Predictors,” Annals of Statistics, 30, 475–497.
   Web of Science ®Google Scholar
• Cook, R. D. (1998), Regression Graphics, New York: Wiley.
   Google Scholar
• Cook, R. D., and Li, L. (2009), “Dimension Redution in Regressions With Exponential Family Predictors,” Journal of Computational and Graphical Statistics, 18, 774–791.
   Web of Science ®Google Scholar
• Cook, R. D., and Weisberg, S. (1991), Comment on “Sliced Inverse Regression for Dimension Reduction” by K.C. Li, Econometrica, 86, 328–332.
   Google Scholar
• Cook, R. D., and Zhang, X. (1991), “Fused Estimators of the Central Subspace in Sufficient Dimension Reduction,” Journal of the American Statistical Association, 109, 815–827.
   Web of Science ®Google Scholar
• Cortez, P., Cordeira, A., Almeida, F., Matos, T., and Reis, J. (2009), “Modeling Wine Preferences by Data Mining From Physicochemical Properties,” Decision Support Systems, 45, 547–553.
   Web of Science ®Google Scholar
• Cosslett, S. R. (1983), “Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model,” Journal of the American Statistical Association, 51, 765–782.
   Google Scholar
• Delecroix, M., Härdle, W., and Hristache, M. (2003), “Efficient Estimation in Conditional Single-Index Regression,” Journal of Multivariate Analysis, 86, 213–226.
   Web of Science ®Google Scholar
• Dong, Y., and Li, B. (2010), “Dimension Reduction for Non-Elliptically Distributed Predictors: Second-Order Moments,” Biometrica, 97, 279–294.
   Web of Science ®Google Scholar
• Edwards, A., and Thurstone, L. (1952), “An Internal Consistency Check for Scale Values Determined by the Method of Successive Intervals,” Psychometrika, 17, 169–180.
   Google Scholar
• Fan, J., and Huang, T. (2005), “Profile Likelihood Inferences on Semiparametric Varying-Coefficient Partially Linear Models,” Bernoulli, 11, 1030–1057.
   Web of Science ®Google Scholar
• Fan, J., and Yim, T. H. (2004), “A Crossvalidation Method for Estimating Conditional Densities,” Biometrika, 91, 819–834.
   Web of Science ®Google Scholar
• Fletcher, R., and Reeves, C. M. (1964), “Function Minimization by Conjugate Gradient,” Comput. J., 7, 149–154.
   Web of Science ®Google Scholar
• Hall, P. (1987), “On Kullback–Leibler Loss and Density Estimation,” Annals of Statistics, 15, 1491–1519.
   Web of Science ®Google Scholar
• Hall, P., and Yao, Q. (2005), “Approximating Conditional Distribution Functions Using Dimension Reduction,” Annals of Statistics, 33, 1404–1421.
   Web of Science ®Google Scholar
• Härdle, W., Hall, P., and Marron, J. S. (1988), “How Far are Automatically Chosen Regression Smoothing Parameters From Their Optimum?” Journal of the American Statistical Association, 83, 86–101.
   Web of Science ®Google Scholar
• Härdle, W., and Marron, J. S. (1985), “Optimal Bandwidth Selection in Nonparametric Regression Function Estimation,” Annals of Statistics, 13, 1465–1481.
   Web of Science ®Google Scholar
• Harrell, F. E., Califf, R. M., Pryor, D. B., Lee, K. L., and Rosati, R. A. (1982), “Evaluating the Yield of Medical Tests,” Journal of the American Medical Association, 247, 2543–2546.
   PubMed Web of Science ®Google Scholar
• Horowitz, J. L., and Härdle, W. (1996), “Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates,” Journal of the American Statistical Association, 91, 1632–1640.
   Web of Science ®Google Scholar
• Huang, M. Y., and Chiang, C. T. (2016), “Estimation and Inference Procedures for Semiparametric Distribution Models With Varying Linear-Index,” Scandinavian Journal of Statistics, doi:10.1111/sjos.12258
   Google Scholar
• Ichimura, H. (1993), “Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models,” Journal of Econometrics, 58, 71–120.
   Web of Science ®Google Scholar
• Jorge, N., and Stephen, J. W. (2006), Numerical Optimization, New York: Springer.
   Google Scholar
• Kong, E., and Xia, Y. (2012), “A Single-Index Quantile Regression Model and Its Estimation,” Econometric Theory, 28, 730–768.
   Web of Science ®Google Scholar
• Kosorok, M. R. (2008), Introduction to Empirical Processes and Semiparametric Inference, New York: Springer.
   Google Scholar
• Le, C. T. (1998), Applied Categorical Data Analysis, New York: Wiley.
   Google Scholar
• Li, B., and Wang, S. (2007), “On Directional Regression for Dimension Reduction,” Journal of the American Statistical Association, 102, 997–1008.
   Web of Science ®Google Scholar
• Li, K. C. (1991), “Sliced Inverse Regression for Dimension Reduction,” Journal of the American Statistical Association, 86, 316–342.
   Web of Science ®Google Scholar
• ——— (1992), “On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein’s Lemma,” Journal of the American Statistical Association, 87, 1025–1039.
   Web of Science ®Google Scholar
• Lo, A. Y. (1991), “Bayesian Bootstrap Clones and a Biometry Function,” Sankhy$\bar{a}$, A53, 320–333.
   Google Scholar
• Ma, Y., and Zhu, L. P. (2012), “A Semiparametric Approach to Dimension Reduction,” Journal of the American Statistical Association, 107, 168–179.
   PubMed Web of Science ®Google Scholar
• ——— (2013), “Efficient Estimation in Sufficient Dimension Reduction,” Annals of Statistics, 41, 250–268.
   PubMed Web of Science ®Google Scholar
• Tsiatis, A. A. (2006), Semiparametric Theory and Missing Data, New York: Springer.
   Google Scholar
• Wang, H., and Xia, Y. (2008), “Sliced Regression for Dimension Reduction,” Journal of the American Statistical Association, 103, 811–821.
   Web of Science ®Google Scholar
• Xia, Y. (2007), “A Constructive Approach to the Estimation of Dimension Reduction Directions,” Annals of Statistics, 35, 2654–2690.
   Web of Science ®Google Scholar
• Xia, Y., Tong, H., Li, W. K., and Zhu, L. X. (2002), “An Adaptive Estimation of Dimension Reduction Space,” Journal of the Royal Statistical Society, Series B, 363–410.
   Google Scholar
• Yin, X., and Li, B. (2011), “Sufficient Dimension Reduction Based on an Ensemble of Minimum Average Variance Estimators,” Annals of Statistics, 39, 3392–3416.
   Web of Science ®Google Scholar
• Zeng, P., and Zhu, Y. (2010), “An Integral Transform Method for Estimating the Central Mean and Central Subspaces,” Journal of Multivariate Analysis, 101, 271–290.
   Web of Science ®Google Scholar
• Zhu, L. P., Yu, Z., and Zhu, L. X. (2010), “A Sparse Eigen-Decomposition Estimation in Semiparametric Regression,” Computational Statistics & Data Analysis, 54, 976–9866.
   Web of Science ®Google Scholar
• Zhu, L. P., Zhu, L. X., and Feng, Z. H. (2010), “Dimension Reduction in Regressions Through Cumulative Slicing Estimation,” Journal of the American Statistical Association, 105, 1455–1466.
   Web of Science ®Google Scholar
• Zhu, L. X., Miao, B., and Peng, H. (2006), “On Sliced Inverse Regression With High-Dimensional Covariates,” Journal of the American Statistical Association, 101, 630–643.
   Web of Science ®Google Scholar
• Zhu, Y., and Zeng, P. (2006), “Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression,” Journal of the American Statistical Association, 101, 1638–1651.
   Web of Science ®Google Scholar