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Articles

Bayesian nonparametric modelling of the link function in the single-index model using a Bernstein–Dirichlet process prior

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Pages 3290-3312 | Received 01 Mar 2019, Accepted 30 Aug 2019, Published online: 10 Sep 2019

References

  • Hardle W, Stoker T. Investigating Smooth Multiple Regression by the Method of Average Derivatives. J Am Stat Assoc. 1989;84(408):986–995.
  • Hardle W, Hall P, Ichimura H. Optimal smoothing in single-index models. Ann Stat. 1993;21(1):157–178. doi: 10.1214/aos/1176349020
  • Ichimura H. Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. J Econom. 1991;58:71–120. doi: 10.1016/0304-4076(93)90114-K
  • Carroll RJ, Fan J, Gijbels I, et al. Generalized partially linear single-index models. J Am Stat Assoc. 1997;92(438):477–489. doi: 10.1080/01621459.1997.10474001
  • Huh J, Park BU. Likelihood-based local polynomial fitting for single-index models. J Multivariate Anal. 2002;80:302–321. doi: 10.1006/jmva.2000.1984
  • Kong E, Xia Y. Quantile estimation of a general single-index model. Statistics. 2008;16(1):33–39.
  • Kuchibhotla AK, Patra RK. Efficient estimation in single index models through smoothing splines; 2017. arXiv preprint arXiv:1612.00068v2.
  • Yu Y, Ruppert D. Penalized spline estimation for partially linear single-index models. J Am Stat Assoc. 2002;97(460):1042–1054. doi: 10.1198/016214502388618861
  • Wang X, Roy V, Zhu Z. A new algorithm to estimate monotone nonparametric link functions and a comparison with parametric approach. Stat Comput. 2018;28:1083–1094. doi: 10.1007/s11222-017-9781-3
  • Antoniadis A, Gregoire G, Mckeague IW. Bayesian estimation in single-index models. Stat Sin. 2004;14(4):1147–1164.
  • Wang HB. Bayesian estimation and variable selection for single index models. Comput Stat Data Anal. 2009;53(7):2617–2627. doi: 10.1016/j.csda.2008.12.010
  • Choi T, Shi JQ, Wang B. A Gaussian process regression approach to a single-index model. J Nonparametr Stat. 2011;23(1):21–36. doi: 10.1080/10485251003768019
  • Gramacy RB, Lian H. Gaussian process single-index models as emulators for computer experiments. Technometrics. 2012;54(1):30–41. doi: 10.1080/00401706.2012.650527
  • Hu Y, Gramacy RB, Lian H. Bayesian quantile regression for single-index models. Stat Comput. 2013;23(4):437–454. doi: 10.1007/s11222-012-9321-0
  • Petrone S. Random Bernstein polynomials. Scand J Stat. 1999;26(3):373–393. Available from: https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9469.00155.
  • Petrone S. Bayesian density estimation using Bernstein polynomials. Can J Stat. 1999;27(1):105–126. Available from: https://onlinelibrary.wiley.com/doi/abs/10.2307/3315494.
  • Petrone S, Wasserman L. Consistency of Bernstein polynomial posteriors. J R Stat Soc. 2002;64(1):79–100. doi: 10.1111/1467-9868.00326
  • Choudhuri N, Ghosal S, Roy A. Bayesian estimation of the spectral density of a time series. J Am Stat Assoc. 2004;99(468):1050–1059. doi: 10.1198/016214504000000557
  • Kirch C, Edwards MC, Meier A, et al. Beyond whittle: nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis. Bayesian Anal. 2018. Available from: https://projecteuclid.org/euclid.ba/1540865702.
  • Sethuraman J. A constructive definition of Dirichlet priors. Stat Sin. 1994;4(2):639–650.
  • Edwards M, Meyer R, Christensen N. Bayesian nonparametric spectral density estimation using b-spline priors. Stat Comput. 2019;29(1):67–78. doi: 10.1007/s11222-017-9796-9
  • Powell JL, Stock JH, Stoker TM. Semiparametric estimation of index coefficients. Econometrica. 1989;57(6):1403–1430. doi: 10.2307/1913713
  • Hristache M, Juditsky A, Spokoiny V. Direct estimation of the index coefficient in a single-index model. Ann Stat. 2001;29(3):595–623. doi: 10.1214/aos/1009210681
  • Naik PA, Tsai CL. Single-index model selections. Biometrika. 2001;88(3):821–832. doi: 10.1093/biomet/88.3.821
  • Peng H, Huang T. Penalized least squares for single index models. J Stat Plan Inference. 2011;141(4):1362–1379. doi: 10.1016/j.jspi.2010.10.003
  • Lv Y, Zhang R, Zhao W, et al. Quantile regression and variable selection for the single-index model. J Appl Stat. 2014;41(7):1565–1577. doi: 10.1080/02664763.2014.881786
  • O'Hara RB, Sillanpää MJ. A review of Bayesian variable selection methods: what, how and which. Bayesian Anal. 2009;4(1):85–117. doi: 10.1214/09-BA403
  • Kuo L, Mallick B. Variable selection for regression models. Sankhya. 1998;60(1):65–81.
  • Koenker R, Machado JA. Goodness of fit and related inference processes for quantile regression. J Am Stat Assoc. 1999;94(448):1296–1310. doi: 10.1080/01621459.1999.10473882
  • Yu K, Moyeed RA. Bayesian quantile regression. Stat Probab Lett. 2001;54(4):437–447. doi: 10.1016/S0167-7152(01)00124-9
  • Kottas A, Gelfand AE. Bayesian semiparametric median regression modeling. Publ Am Stat Assoc. 2001;96(456):1458–1468. doi: 10.1198/016214501753382363
  • Kottas A, Krnjajic M. Bayesian semiparametric modelling in quantile regression. Scand J Stat. 2009;36(2):297–319. doi: 10.1111/j.1467-9469.2008.00626.x
  • Ghosal S. Fundamentals of nonparametric bayesian inference; 2016. Cambridge Series on Statistical and Probabilistic Mathematics; 44.
  • Edwards MC, Meyer R, Christensen N. Bayesian semiparametric power spectral density estimation with applications in gravitational wave data analysis. Phys Rev D. 2015 Sep;92:064011. Available from: https://link.aps.org/doi/10.1103/PhysRevD.92.064011.
  • Kozubowski TJ, Podgorski K. A multivariate and asymmetric generalization of Laplace distribution. Comput Stat. 2000;15(4):531–540.
  • Lum K, Gelfand AE. Spatial quantile multiple regression using the asymmetric Laplace process. Bayesian Anal. 2012;7(2):235–258. doi: 10.1214/12-BA708
  • Kuchibhotla AK, Patra RK, Sen B. Efficient estimation in convex single index models; 2016. R package version 06.
  • Gramacy RB. tgp: an r package for Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian process models. J Stat Softw. 2007;19(i09).
  • Gramacy RB, Taddy MA, Leeuw JD. Categorical inputs, sensitivity analysis, optimization and importance tempering with tgp version 2, an r package for treed Gaussian process models. J Stat Softw. 2010;33(i06):1–48.
  • Wu TZ, Yu K, Yu Y. Single-index quantile regression. J Multivar Anal. 2010;101(7):1607–1621. doi: 10.1016/j.jmva.2010.02.003
  • Kong E, Xia Y. A single-index quantile regression model and its estimation. Econ Theory. 2012;28(4):730–768. doi: 10.1017/S0266466611000788
  • Feng Z, Zhu L. An alternating determination–optimization approach for an additive multi-index model. Comput Stat Data Anal. 2012;56(6):1981–1993. doi: 10.1016/j.csda.2011.12.004
  • Liang R. Urban sewage treatment plant energy consumption influence factors research [Master's thesis]. Beijing Jiaotong University; 2014.
  • Ren F, Mao L, Fu W, et al. Study of influent factors on energy consumption of municipal wastewater treatment plant operation in China. Water Wastewater Eng. 2015;41(1):42–47.
  • Yu Y, Zou Z, Wang S. Statistical regression modeling for energy consumption in wastewater treatment. J Environ Sci. 2018;75:201–208. doi: 10.1016/j.jes.2018.03.023

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