Sufficient Dimension Folding for Regression Mean Function

REFERENCES

• Albert, S.P., Shih, H.J. (2010), An Approach for Jointly Modeling Multivariate Longitudinal Measurements and Discrete Time-to-Event Data, The Annals of Applied Statistics, 4, 1517–1532.
   PubMed Web of Science ®Google Scholar
• Cook, R.D. (1994), On the Interpretation of Regression Plots, Journal of the American Statistical Association, 89, 177–190.
   Web of Science ®Google Scholar
• ——— (1996), Graphics for Regressions With a Binary Response, Journal of the American Statistical Association, 91, 983–992.
   Web of Science ®Google Scholar
• ——— (1998), Regression Graphics: Ideas for Studying Regressions Through Graphics, New York: Wiley.
   Google Scholar
• Cook, R.D., Li, B. (2002), Dimension Reduction for Conditional Mean in Regression, The Annals of Statistics, 30, 455–474.
   Web of Science ®Google Scholar
• Cook, R.D., Weisberg, S. (1991), Discussion of “Sliced Inverse Regression for Dimension Reduction,” Journal of the American Statistical Association, 86, 28–33.
   Web of Science ®Google Scholar
• Ding, S., Cook, R.D. (2014), Dimension Folding PCA and PFC for Matrix-Valued Predictors, Statistica Sinica, 24, 463–492.
   Web of Science ®Google Scholar
• Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and its Applications, London: Chapman & Hall.
   Google Scholar
• Fan, J., and Yao, Q. (2003), Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag.
   Google Scholar
• Fan, J., Yao, Q., Cai, Z. (2003), Adaptive Varying-Coefficient Linear Models, Journal of the Royal Statistical Society, Series B, 65, 57–80.
   Google Scholar
• Fleming, R.T., and Harrington, P.D. (1991), Counting Process and Survival Analysis, New York: Wiley.
   Google Scholar
• Kim, R.W., Wiesner, H.R., Poterucha, J.J., Therneau, M.T., Benson, T.J., Krom, A. F.R., Dickson, R.E. (2000), Adaptation of the Mayo Primary Biliary Cirrhosis Natural History Model for Application in Liver Transplant Candidates, Liver Transplantation, 6, 489–494.
   PubMed Web of Science ®Google Scholar
• Li, B., Cook, R.D., Chiaromonte, F. (2003), Dimension Reduction for the Conditional Mean in Regression With Categorical Predictors, The Annals of Statistics, 31, 1636–1668.
   Web of Science ®Google Scholar
• Li, B., Kim, M., Altman, N. (2010), On Dimension Folding of Matrix- or Array-Valued Statistical Objects, The Annals of Statistics, 38, 1094–1121.
   Web of Science ®Google Scholar
• Li, B., Wang, S. (2007), On Directional Regression for Dimension Reduction, Journal of the American Statistical Association, 102, 997–1008.
   Web of Science ®Google Scholar
• Li, B., Wen, S., Zhu, L. (2008), On a Projective Resampling Method for Dimension Reduction With Multivariate Responses, Journal of the American Statistical Association, 103, 1177–1186.
   Web of Science ®Google Scholar
• Li, B., Zha, H., Chiaromonte, F. (2005), Contour Regression: A General Approach to Dimension Reduction, The Annals of Statistics, 33, 1580–1616.
   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
• Li, L., Yin, X. (2009), Longitudinal Data Analysis Using Sufficient Dimension Reduction Method, Computational Statistics and Data Analysis, 53, 4106–4115.
   Web of Science ®Google Scholar
• Lu, N., Zimmerman, L.D. (2005), The Likelihood Ratio Test for a Separable Covariance Matrix, Statistics & Probability Letters, 73, 449–457.
   Web of Science ®Google Scholar
• Müller, G.H. (2005), Functional Modelling and Classification of Longitudinal Data, Scandinavian Journal of Statistics, 32, 223–240.
   Web of Science ®Google Scholar
• Murtaugh, A.P., Dickson, R.E., Van Dam, M.G., Malinchoc, M., Grambsch, M.P., Langworthy, L.A., Gips, H.C. (1994), Primary Biliary Cirrhosis: Prediction of Short-Term Survival Based on Repeated Patient Visits, Hepatology, 20, 126–136.
   PubMed Web of Science ®Google Scholar
• Pfeiffer, M.R., Forzani, L., Bura, E. (2011), Sufficient Dimension Reduction for Longitudinally Measured Predictors, Statistics in Medicine, 22, 2414–2427.
   Google Scholar
• Shapiro, M.J., Smith, H., Schaffner, F. (1979), Serum Bilirubin: A Prognostic Factor in Primary Biliary Cirrhosis, Gut, 20, 137–140.
   PubMed Web of Science ®Google Scholar
• Silverman, W.B. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman & Hall.
   Google Scholar
• Srivastava, S.M., von Rosen, T., von Rosen, D. (2008), Models With a Kronecker Product Covariance Structure: Estimation and Testing, Mathematical Methods of Statistics, 17, 357–370.
   Google Scholar
• ——— (2009), Estimation and Testing in General Multivariate Linear Models With Kronecker Product Covariance Structure, The Indian Journal of Statistics, 71-A(Part 2), 137–163.
   Google Scholar
• Wang, H., Xia, Y. (2008), Sliced Regression for Dimension Reduction, Journal of the American Statistical Association, 103, 811–821.
   Web of Science ®Google Scholar
• Wang, Q., Yin, X. (2008), A Nonlinear Multi-Dimensional Variable Selection Method for High Dimensional Data: Sparse MAVE, Computational Statistics and Data Analysis, 52, 4512–4520.
   Web of Science ®Google Scholar
• Xia, Y. (2007), A Constructive Approach to the Estimation of Dimension Reduction Directions, The Annals of Statistics, 35, 2654–2690.
   Web of Science ®Google Scholar
• Xia, Y., Tong, H., Li, W., Zhu, L. (2002), An Adaptive Estimation of Dimension Reduction, Journal of Royal Statistical Society, Series B, 64, 363–410.
   Google Scholar
• Yin, X., Li, B. (2011), Sufficient Dimension Reduction Based on an Ensemble of Minimum Average Variance Estimators, The Annals of Statistics, 39, 3392–3416.
   Web of Science ®Google Scholar
• Yin, X., Li, B., Cook, D.R. (2008), Successive Direction Extraction for Estimating the Central Subspace in a Multiple-Index Regression, Journal of Multivariate Analysis, 99, 1773–1757.
   Web of Science ®Google Scholar
• Zhu, L., Miao, B., 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