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Original Articles

Nonparametric estimation of varying-coefficient single-index models

Pages 281-291 | Received 29 Jun 2013, Accepted 18 Jul 2014, Published online: 12 Aug 2014

References

  • I. Ahmad, S. Leelahanon, and Q. Li, Efficient estimation of a semiparametric partially linear varying coefficient model, Ann. Stat. 33 (2005), pp. 258–283. doi: 10.1214/009053604000000931
  • C.T. Chiang, J.A. Rice, and C.O. Wu, Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables, J. Am. Statist. Assoc. 93 (2001), pp. 961–994.
  • P.P.B. Eggermont, R.L. Eubank, and V.N. LaRiccia, Convergence rates for smoothing spline estimators in varying coefficient models, J. Statist. Plann. Inference 140 (2010), pp. 369–381. doi: 10.1016/j.jspi.2009.06.017
  • J. Fan and T. Huang, Profile likelihood inference on semiparametric varying-coefficient partially linear models, Bernoulli 11 (2005), pp. 1031–1057. doi: 10.3150/bj/1137421639
  • C. Gu, Smoothing Spline ANOVA models, 2nd ed., Springer, New York, 2013.
  • C. Gu and Y.-J. Kim, Penalized likelihood regression: General formulation and efficient approximation, Can. J. Stat. 30 (2002), pp. 619–628. doi: 10.2307/3316100
  • W. Hardle and T.M. Stoker, Investigating smooth multiple regression by the method of average derivatives, J. Am. Statist. Assoc. 84 (1989), pp. 986–995.
  • W. Hardle, P. Hall, and H. Ichimura, Optimal smoothing in single-index models, Ann. Stat. 21 (1993), pp. 157–178. doi: 10.1214/aos/1176349020
  • T.J. Hastie and R. Tibshirani, Varying-coefficient models, J. R. Stat. Soc. Ser. B 55 (1993), pp. 757–796.
  • T.J. Hastie, R. Tibshirani, and J. Friedman, The elements of statistical learning, Springer, New York, 2001.
  • D.R. Hoover, J.A. Rice, C.O. Wu, and L-P. Yang, Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data, Biometricka 85 (1998), pp. 809–822. doi: 10.1093/biomet/85.4.809
  • M. Hristache, A. Juditsky, J. Polzehl, and V. Spokoiny, Structure adaptive approach for dimension reduction, Ann. Stat. 29 (2001), pp. 1537–1566.
  • T. Hu and Y. Xia, Adpative semi-varying coefficient model selection, Statist. Sin. 22 (2012), pp. 575–599.
  • Z. Huang, Efficient inferences on the varying-coefficient single-index model with empirical likelihood, Comput. Statist. Data Anal. 56 (2012), pp. 4413–4420. doi: 10.1016/j.csda.2012.03.024
  • Z. Huang and R. Zhang, Empirical likelihood for the varying-coefficient single-index model, Can. J. Stat. 38 (2010), pp. 434–452. doi: 10.1002/cjs.10075
  • Y-J. Kim, A partial spline approach for semiparametric estimation of varying-coefficient partially linear models, Comput. Stat. Data Anal. 62 (2013), pp. 181–187. doi: 10.1016/j.csda.2013.01.006
  • Y-J. Kim and C. Gu, Smoothing spline Gaussian regression: More scalable computation via efficient approximation, J. R. Statist. Soc. Ser. B 66 (2004), pp. 337–356. doi: 10.1046/j.1369-7412.2003.05316.x
  • F. Leitenstorfer and G. Tutz, Estimation of single-index models based on boosting techniques, Stat. Model. 11 (2011), pp. 203–217. doi: 10.1177/1471082X1001100302
  • C. Leng, A simple approach for varying-coefficient model selection, J. Statist. Plann. Inference 139 (2009), pp. 2138–2146. doi: 10.1016/j.jspi.2008.10.009
  • D. Nychka, Bayesian confidence intervals for smoothing splines, J. Am. Statist. Assoc. 83 (1988), pp. 1134–1143. doi: 10.1080/01621459.1988.10478711
  • J. Polzehl and S. Sperlich, A note on structural adaptive dimension reduction, J. Statist. Comput. Simul. 79 (2009), pp. 805–818. doi: 10.1080/00949650801959699
  • G. Wahba, Bayesian confidence interval for the cross-validated smoothing spline, J. R. Statist. Soc. Ser. B 45 (1983), pp. 133–150.
  • Q. Wang and L. Xue, Statistical inference in partially-varying-coefficient single-index model, J. Multivariate Anal. 102 (2011), pp. 1–19. doi: 10.1016/j.jmva.2010.07.005
  • H. Wong, W-C. Ip, and R. Zhang, Varying-coefficient single-index model, Comput. Statist. Data Anal. 52 (2008), pp. 1458–1476. doi: 10.1016/j.csda.2007.04.008
  • Y. Xia, H. Tong, W. K. Li, and L. Zhn, An adaptive estimation of dimension reduction, J. R. Statist. Soc. Ser. B 64 (2002), pp. 363–410. doi: 10.1111/1467-9868.03411
  • Y. Xia, W. Zhang, and H. Tong, Efficient estimation for semivarying-coefficient models, Biometrika 91 (2004), pp. 661–681. doi: 10.1093/biomet/91.3.661
  • Y. Yu and D. Ruppert, Penalized spline estimation for partially linear single-index models, J. Am. Statist. Assoc. 97 (2002), pp. 1042–1054. doi: 10.1198/016214502388618861

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