Sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects

References

• Čížek, P., and Härdle, W. (2006), ‘Robust Estimation of Dimension Reduction Space’, Computational Statistics and Data Analysis, 51, 545–555. doi: 10.1016/j.csda.2005.11.001
   Web of Science ®Google Scholar
• Cook, R.D. (1998), Regression Graphics, New York: Wiley.
   Google Scholar
• Ding, S., and 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
• Fu, L., and Wang, Y.-G . (2012), ‘Quantile Regression for Longitudinal Data with a Working Correlation Model’, Computational Statistics and Data Analysis, 56, 2526–2538. doi: 10.1016/j.csda.2012.02.005
   Web of Science ®Google Scholar
• Geraci, M., and Bottai, M. (2007), ‘Quantile Regression for Longitudinal Data using the Asymmertic Laplace Distribution’, Biostatistics, 8, 140–154. doi: 10.1093/biostatistics/kxj039
   PubMed Web of Science ®Google Scholar
• Huber, P.J. (1964), ‘Robust Estimation of a Location Parameter’, The Annals of Mathematical Ststistics, 35, 73–101. doi: 10.1214/aoms/1177703732
   Google Scholar
• Kai, B., Li, Z., and Zou, H. (2010), ‘Local Composite Quantile Regression Smoothing: an Efficient and Safe Alternative to Local Polynomial Regression’, Journal of Royal Statistical Society, Series B, 72, 49–69. doi: 10.1111/j.1467-9868.2009.00725.x
   Google Scholar
• Koenker, R. (2004), ‘Quantile Regression for Longitudinal Data’, Journal of Multivariate Analysis, 91, 74–89. doi: 10.1016/j.jmva.2004.05.006
   Web of Science ®Google Scholar
• Koenker, R. (2005), Quantile Regression, New York: Cambridge University Press.
   Google Scholar
• Koenker, R., Ng, P., and Portnoy, S. (1994), ‘Quantile Smoothing Splines’, Biometrika, 8, 673–680. doi: 10.1093/biomet/81.4.673
   Google Scholar
• Kong, E., and Xia, Y. (2012), ‘A Single-Index Quantile Regression Model and its Estimation’, Econometric Theory, 28, 730–768. doi: 10.1017/S0266466611000788
   Web of Science ®Google Scholar
• Lee, J.S., and Cox, D.D. (2010), ‘Robust Smoothing: Smoothing Parameter Selection and Applications to Fluorescence Spectroscopy’, Computational Statistics and Data Analysis, 54, 3131–3143. doi: 10.1016/j.csda.2009.08.001
   PubMed Web of Science ®Google Scholar
• Li, B., Kim, M., and Altman, N. (2010), ‘On Dimension Folding of Matrix- or Array-Valued Statistical Objects’, The Annals of Statistics, 38, 1094–1121. doi: 10.1214/09-AOS737
   Web of Science ®Google Scholar
• Li, B., Wen, S., and Zhu, L. (2008), ‘On a Projective Resampling Method for Dimension Reduction with Multivariate Responses’, Journal of the American Statistical Association, 103, 1177–1186. doi: 10.1198/016214508000000445
   Web of Science ®Google Scholar
• Li, B., Zha, H., and Chiaromonte, F. (2005), ‘Contour Regression: a General Approach to Dimension Reduction’, The Annals of Statistics, 33, 1580–1616. doi: 10.1214/009053605000000192
   Web of Science ®Google Scholar
• Li, K.-C. (1991), ‘Sliced Inverse Regression for Dimension Reduction’, Journal of the American Statistical Association, 86, 316–342. doi: 10.1080/01621459.1991.10475035
   Web of Science ®Google Scholar
• Li, L., and Yin, X. (2008), ‘Sliced Inverse Regression with Regularizations’, Biometrics, 64, 124–131. doi: 10.1111/j.1541-0420.2007.00836.x
   PubMed Web of Science ®Google Scholar
• Luo, W., Li, B., and Yin, X. (2014), ‘On Efficient Dimension Reduction with Respect to a Statistical Functional of Interest’, The Annals of Statistics, 42, 382–412. doi: 10.1214/13-AOS1195
   Web of Science ®Google Scholar
• Oh, H.-S., Nychka, D., Brown, T., and Charbonneau, P. (2004), ‘Period Analysis of Variable Stars by Robust Smoothing’, Journal of the Royal Statistical Society, Series C, 53, 15–30. doi: 10.1111/j.1467-9876.2004.00423.x
   Web of Science ®Google Scholar
• Pfeiffer, R.M., Forzani, L., and Bura, E. (2011), ‘Sufficient Dimension Reduction for Longitudinally Measured Predictors’, Statistics in Medicine, 22, 2414–2427.
   Google Scholar
• Schott, R.J. (1997), Matrix Analysis for Statistics, New York: Wiley.
   Google Scholar
• Shapiro, J.M., Smith, H., and Schaffner, F. (1979), ‘Serum Bilirubin: A Prognostic Factor in Primary Biliary Cirrhosis’, Gut, 20, 137–140. doi: 10.1136/gut.20.2.137
   PubMed Web of Science ®Google Scholar
• Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman & Hall.
   Google Scholar
• Tibshirani, R. (1996), ‘Regression Shrinkage and Selection Via the Lasso’, Journal of Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• Wang, Q., and Yin, X. (2008), ‘A Nonlinear Multi-Dimensional Variable Selection Method for High Dimensional Data: Sparse MAVE’, Computational Statistics and Data Analysis, 52, 4512–4520. doi: 10.1016/j.csda.2008.03.003
   Web of Science ®Google Scholar
• Wu, T. Z., Yu, K., and Yu, Y. (2010), ‘Single-Index Quantile Regression’, Journal of Multivariate Analysis, 101, 1607–1621. doi: 10.1016/j.jmva.2010.02.003
   Web of Science ®Google Scholar
• Xia, Y., Tong, H., Li, W., and Zhu, L. (2002), ‘An Adaptive Estimation of Dimension Reduction’, Journal of Royal Statistical Society, Series B, 64, 363–410. doi: 10.1111/1467-9868.03411
   Google Scholar
• Xue, Y., and Yin, X. (2014), ‘Sufficient Dimension Folding for Regression Mean Function’, Journal of Computational and Graphical Statistics, 23, 1028–1043. doi: 10.1080/10618600.2013.859619
   Web of Science ®Google Scholar
• Yin, X., Li, B., and Cook, R.D. (2008), ‘Successive Direction Extraction for Estimating the Central Subspace in a Multiple-Index Regression’, Journal of Multivariate Analysis, 99, 1773–1757. doi: 10.1016/j.jmva.2008.01.006
   Web of Science ®Google Scholar
• Yu, K., and Jones, M.C. (1998), ‘Local Linear Quantile Regression’, Journal of the American Statistical Association, 93, 228–237. doi: 10.1080/01621459.1998.10474104
   Web of Science ®Google Scholar
• Zhu, L., Miao, B., and Peng, H. (2006), ‘On Sliced Inverse Regression with High-Dimensional Covariates’, Journal of the American Statistical Association, 101, 630–643. doi: 10.1198/016214505000001285
   Web of Science ®Google Scholar
• Zou, H., and Yuan, M. (2008), ‘Composite Quantile Regression and the Oracle Model Selection Theory’, The Annals of Statistics, 36, 1108–1126. doi: 10.1214/07-AOS507
   Web of Science ®Google Scholar