Multivariate partially linear single-index models: Bayesian analysis

References

• Antoniadis, A., Grégoire, G., and McKeague, I.W. (2004), ‘Bayesian Estimation in Single-Index Models’, Statistica Sinica, 14, 1147–1164.
   Web of Science ®Google Scholar
• Biller, C. (2000), ‘Adaptive Bayesian Regression Spline in Semiparamtric Generalized Linear Models’, Journal of Computational and Graphical Statistics, 9, 122–140.
   Web of Science ®Google Scholar
• Box, G.E.P., and Draper, N.R. (1987), Empirical Model-Building and Response Surfaces, New York: Wiley.
   Google Scholar
• Carroll, R.J., Fan, J, Gijbels, I., and Wand, M.P. (1997), ‘Generalized Partially Linear Single-Index Models’, Journal of the American Statistical Association, 92, 477–489. doi: 10.1080/01621459.1997.10474001
   Web of Science ®Google Scholar
• Chinchilli, V., Schwab, B., and Sen, P. (1989), ‘Inference Based on Ranks for the Multiple-Design Multivariate Linear Model’, Journal of the American Statistical Association, 84, 517–524. doi: 10.1080/01621459.1989.10478798
   Web of Science ®Google Scholar
• Choi, T., Shi, J., and Wang, B. (2011), ‘A Gaussian Process Regression Approach to A Single-Index Model’, Journal of Nonparametric Statistics, 23, 21–36. doi: 10.1080/10485251003768019
   Web of Science ®Google Scholar
• Denison, D.G.T., Mallick, B.K., and Smith, A.F.M. (1998), ‘Automatic Bayesian Curving Fitting’, Journal of the Royal Statistical Society, Series B, 60, 333–350. doi: 10.1111/1467-9868.00128
   Google Scholar
• Dimatteo, I., Genovese, C.R., and Kass, R.E. (2001), ‘Bayesian Curve Fitting with Free-Knot Splines’, Biometrika, 88, 1055–1071. doi: 10.1093/biomet/88.4.1055
   Web of Science ®Google Scholar
• Engle, R.F., Granger, C.W, Rice, J., and Weiss, A. (1986), ‘Semiparametric Estimates of the Relation Between Weather and Electricity Sales’, Journal of the American Statistical Association, 81, 310–320. doi: 10.1080/01621459.1986.10478274
   Web of Science ®Google Scholar
• Gelman, A., and Rubin, D.B. (1992), ‘Inference from Iterative Simulation Using Multiple Sequences’, Statistical Science, 7, 457–472. doi: 10.1214/ss/1177011136
   Google Scholar
• Gramacy, R., and Lian, H. (2011), ‘Gaussian Process Single-Index Models as Emulators for Computer Experiments’, Technometrics, 54, 30–41. doi: 10.1080/00401706.2012.650527
   Web of Science ®Google Scholar
• Green, P. (1995), ‘Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination’, Biometrika, 82, 711–732. doi: 10.1093/biomet/82.4.711
   Web of Science ®Google Scholar
• Härdle, W., Hall, P., and Ichimura, H. (1993), ‘Optimal Smoothing in Single-Index Models’, The Annals of Statistics, 21, 157–178. doi: 10.1214/aos/1176349020
   Web of Science ®Google Scholar
• Härdle, W., and Stoker, T.M. (1989), ‘Investigating Smooth Multiple Regression by the Method of Average Derivatives’, Journal of the American Statistical Association, 84, 986–995.
   Web of Science ®Google Scholar
• Hastie, T.J., and Tibshirani, R.J. (1990), ‘Generalized Additive Models’, London: Chapman and Hall.
   Google Scholar
• Holmes, C.C., and Mallick, B.K. (2001), ‘Bayesian Regression with Multivariate Linear Splines’, Journal of the Royal Statistical Society, Series B, 63, 3–17. doi: 10.1111/1467-9868.00272
   Google Scholar
• Holmes, C.C., and Mallick, B.K. (2003), ‘Generalized Nonlinear Modeling with Multivariate Free-Knot Regression Splines’, Journal of the American Statistical Association, 98, 352–368. doi: 10.1198/016214503000143
   Web of Science ®Google Scholar
• Horowitz, J.L. (1998), Semiparametric Methods in Econometrics, New York: Springer.
   Google Scholar
• Ichimura, H. (1993), ’Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models’, Journal of Econometrics, 58, 71–120. doi: 10.1016/0304-4076(93)90114-K
   Web of Science ®Google Scholar
• Kong, E., and Xia, Y. (2007), ‘Variable Selection for the Single-Index Model’, Biometrika, 94, 217–229. doi: 10.1093/biomet/asm008
   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, Y.-H., Wang, N.-Y., and Carroll, R. J. (2010), ‘Generalized Functional Linear Models with Semiparametric Single-Index Interactions’,Journal of the American Statistical Association, 105, 621–633. doi: 10.1198/jasa.2010.tm09313
   PubMed Web of Science ®Google Scholar
• Liang, H., and Wang, N.-Y. (2005), ‘Partially Linear Single-Index Measurement Error Models’, Statistica Sinica, 15, 99–116.
   Web of Science ®Google Scholar
• Liang, H., Liu, X., Li, R., and Tsai, C.-L. (2010), ‘Estimation and Testing for Partially Linear Single-Index Models’, The Annals of Statistics, 38, 3811–3836. doi: 10.1214/10-AOS835
   PubMed Web of Science ®Google Scholar
• Lin, W., and Kulasekera, K.B. (2010), ‘Testing the Equality of Linear Single-Index Models’, Journal of Multivariate Analysis, 101, 1156–1167. doi: 10.1016/j.jmva.2009.10.006
   Web of Science ®Google Scholar
• Lindstrom, M.J. (2002), ‘Bayesian Estimation of Free-Knot Splines Using Reversible Jump’, Computational Science & Data Analysis, 41, 255–269. doi: 10.1016/S0167-9473(02)00066-X
   Web of Science ®Google Scholar
• Liu, J.S. (1994), ‘The Collapsed Gibbs Sampler in Bayesian Computations with Applications to A Gene Regulation Problem’, Journal of the American Statistical Association, 89, 958–966. doi: 10.1080/01621459.1994.10476829
   Web of Science ®Google Scholar
• Lopez, O. (2009), ‘Single-Index Regression Models with Right-Censored Responses’, Journal of Statistical Planning and Inference, 139, 1082–1097. doi: 10.1016/j.jspi.2008.06.012
   Web of Science ®Google Scholar
• Lu, X.-W., and Cheng, T.-L. (2007), ‘Randomly Censored Partially Linear Single-Index Models’, Journal of Multivariate Analysis, 98, 1895–1922. doi: 10.1016/j.jmva.2006.11.008
   Web of Science ®Google Scholar
• Madigan, D., and Raftery, A.E. (1994), ‘Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window’, Journal of the American Statistical Association, 89, 1535–1 546. doi: 10.1080/01621459.1994.10476894
   Web of Science ®Google Scholar
• McCullagh, P., and Nelder, J.A. (1989), ’Generalized Linear Models’ (2nd ed.), London: Chapman and Hall.
   Google Scholar
• McDonald, L. (1975), ‘Tests for the General Linear Hypothesis under the Multiple Design Multivariate Linear Model’, The Annals of Statistics, 3, 461–466. doi: 10.1214/aos/1176343072
   Web of Science ®Google Scholar
• Naik, P.A., and Tsai, C.L. (2001), ‘Single-Index Model Selections’, Biometrika, 88, 821–832. doi: 10.1093/biomet/88.3.821
   Web of Science ®Google Scholar
• Poon, W.-Y., and Wang, H.-B. (2013), ‘Bayesian Analysis of Generalized Partially Linear Single-Index Models’, Computational Statistics and Data Analysis, 68, 251–261. doi: 10.1016/j.csda.2013.07.018
   Web of Science ®Google Scholar
• Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997), ‘Bayesian Model Averaging for Linear Regression Models’, Journal of the American Statistical Association, 92, 179–191. doi: 10.1080/01621459.1997.10473615
   Web of Science ®Google Scholar
• Smith, M., and Kohn, R. (1996), ‘Nonparametric Regression Using Bayesian Variable Selection’, Journal of Econometric, 75, 317–344. doi: 10.1016/0304-4076(95)01763-1
   Web of Science ®Google Scholar
• Stoker, T. (1986), ‘Consistent Estimation of Scaled Coefficients’, Econometrica, 54, 1461–1481. doi: 10.2307/1914309
   Web of Science ®Google Scholar
• van Dyk, D., and Park, T. (2008), ‘Partially Collapsed Gibbs Samplers: Theory and Methods’, Journal of the American Statistical Association, 103, 790–796. doi: 10.1198/016214508000000409
   Web of Science ®Google Scholar
• Wang, H.-B. (2009), ‘Bayesian Estimation and Variable Selection for Single-Index Models’, Computational Statistics and Data Analysis, 53, 2617–2627. doi: 10.1016/j.csda.2008.12.010
   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., and Li, W. K. (1999), ‘On Extended Partially Linear Single-Index Models’, Biometrika, 86, 831–842. doi: 10.1093/biomet/86.4.831
   Web of Science ®Google Scholar
• Xia, Y., Tong, H., Li, W.K., and Zhu, L. (2002), ‘An Adaptive Estimation of Dimension Reduction Space (with Discussion)’, Journal of the Royal Statistical Society, Series B 64, 363–410. doi: 10.1111/1467-9868.03411
   Google Scholar
• Yu, Y., and Ruppert, D. (2002), ‘Penalized Spline Estimation for Partially Linear Single-Index Model’, Journal of the American Statistical Association, 97, 1042–1054. doi: 10.1198/016214502388618861
   Web of Science ®Google Scholar
• Zhu, L.-X., and Xue, L.-G. (2006), ‘Empirical Likelihood Confidence Regions in A Partially Linear Single-Index Model’, Journal of the Royal Statistical Society, Ser. B 68, 549–570. doi: 10.1111/j.1467-9868.2006.00556.x
   Google Scholar