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Research Article

Estimation and hypothesis test for varying coefficient single-index multiplicative models

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Received 14 Aug 2023, Accepted 19 May 2024, Published online: 29 May 2024

References

  • Chen K, Lin Y, Wang Z, et al. Least product relative error estimation. J Multivar Anal. 2016;144:91–98. doi: 10.1016/j.jmva.2015.10.017
  • Liu H, Xia X. Estimation and empirical likelihood for single-index multiplicative models. J Stat Plan Inference. 2018;193:70–88. doi: 10.1016/j.jspi.2017.08.003
  • Zhang J, Zhu J, Feng Z. Estimation and hypothesis test for single-index multiplicative models. Test. 2019;28(1):242–268. doi: 10.1007/s11749-018-0586-2
  • Fan J, Huang T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli. 2005;11(6):1031–1057. doi: 10.3150/bj/1137421639
  • Fan J, Yao Q, Cai Z. Adaptive varying-coefficient linear models. J R Stat Soc B: Stat Methodol. 2003;65(1):57–80. doi: 10.1111/1467-9868.00372
  • Fan J, Zhang W. Statistical estimation in varying coefficient models. Ann Stat. 1999;27(5):1491–1518. doi: 10.1214/aos/1017939139
  • Fan J, Zhang W. Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scand J Stat. 2000;27(4):715–731. doi: 10.1111/sjos.2000.27.issue-4
  • Hastie T, Tibshirani R. Varying-coefficient models. J R Stat Soc Series B Stat Methodol. 1993;55(4):757–779. doi: 10.1111/j.2517-6161.1993.tb01939.x
  • Lee YK, Mammen E, Park BU. Flexible generalized varying coefficient regression models. Ann Stat. 2012;40(3):1906–1933. doi: 10.1214/12-AOS1026
  • Lee YK, Mammen E, Park BU. Projection-type estimation for varying coefficient regression models. Bernoulli. 2012;18(1):177–205. doi: 10.3150/10-BEJ331
  • Park BU, Mammen E, Lee YK, et al. Varying coefficient regression models: a review and new developments. Int Stat Rev. 2015;83(1):36–64. doi: 10.1111/insr.v83.1
  • Zhang W, Peng H. Simultaneous confidence band and hypothesis test in generalised varying-coefficient models. J Multivar Anal. 2010;101(7):1656–1680. doi: 10.1016/j.jmva.2010.03.003
  • Zhao J, Peng H, Huang T. Variance estimation for semiparametric regression models by local averaging. Test. 2018;27(2):453–476. doi: 10.1007/s11749-017-0553-3
  • Zhao W, Lian H, Liang H. Quantile regression for the single-index coefficient model. Bernoulli. 2017;23(3):1997–2027. doi: 10.3150/16-BEJ802
  • Chen K, Guo S, Lin Y, et al. Least absolute relative error estimation. J Am Stat Assoc. 2010;105(491):1104–1112. doi: 10.1198/jasa.2010.tm09307
  • Zhang J, Cui X, Peng H. Estimation and hypothesis test for partial linear single-index multiplicative models. Ann Inst Stat Math. 2019;72(3):699–740. doi: 10.1007/s10463-019-00706-6
  • Fan J, Peng H. Nonconcave penalized likelihood with a diverging number of parameters. Ann Stat. 2004;32(3):928–961. doi: 10.1214/009053604000000256
  • Cui X, Härdle WK, Zhu L. The EFM approach for single-index models. Ann Stat. 2011;39(3):1658–1688. doi: 10.1214/10-AOS871
  • Feng S, Kong K, Kong Y, et al. Statistical inference of heterogeneous treatment effect based on single-index model. Comput Stat Data Anal. 2022;175:Article ID 107554. doi: 10.1016/j.csda.2022.107554
  • Gai Y, Zhang J. Single-index relative error regression models. Commun Stat – Simul Comput. 2022;51(5):2252–2267. doi: 10.1080/03610918.2021.1982972
  • Li G, Lai P, Lian H. Variable selection and estimation for partially linear single-index models with longitudinal data. Stat Comput. 2015;25(3):579–593. doi: 10.1007/s11222-013-9447-8
  • Li G, Peng H, Dong K, et al. Simultaneous confidence bands and hypothesis testing for single-index models. Stat Sin. 2014;24(2):937–955.
  • Lian H, Liang H. Separation of linear and index covariates in partially linear single-index models. J Multivar Anal. 2016;143:56–70. doi: 10.1016/j.jmva.2015.08.017
  • Lian H, Liang H, Carroll RJ. Variance function partially linear single-index models. J R Stat Soc B: Stat Methodol. 2015;77(1):171–194. doi: 10.1111/rssb.12066
  • 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
  • Zhang J, Gai Y, Lin B. Detection of marginal heteroscedasticity for partial linear single-index models. Commun Stat – Simul Comput. 2021;50(3):724–743. doi: 10.1080/03610918.2019.1565585
  • Zhang J, Niu C, Lu T, et al. Estimation of the error distribution function for partial linear single-index models. Commun Stat – Simul Comput. 2020;49(1):29–44. doi: 10.1080/03610918.2018.1468461
  • Bindele HF, Abebe A, Meyer KN. General rank-based estimation for regression single index models. Ann Inst Stat Math. 2018;70(5):1115–1146. doi: 10.1007/s10463-017-0618-9
  • Boente G, Rodriguez D. Robust estimates in generalized partially linear single-index models. Test. 2012;21(2):386–411. doi: 10.1007/s11749-011-0249-z
  • Feng S, Tian P, Hu Y, et al. Estimation in functional single-index varying coefficient model. J Stat Plan Inference. 2021;214:62–75. doi: 10.1016/j.jspi.2021.01.003
  • Feng S, Xue L. Model detection and estimation for single-index varying coefficient model. J Multivar Anal. 2015;139:227–244. doi: 10.1016/j.jmva.2015.03.008
  • Feng S, Xue L. Partially functional linear varying coefficient model. Statistics. 2016;50:717–732. doi: 10.1080/02331888.2016.1138954
  • Liang H, Liu X, Li R, et al. Estimation and testing for partially linear single-index models. Ann Stat. 2010;38:3811–3836.
  • Xia Y, Li WK. On single-index coefficient regression models. J Am Stat Assoc. 1999;94:1275–1285. doi: 10.1080/01621459.1999.10473880
  • Bierens HJ. Consistent model specification tests. J Econom. 1982;20:105–134. doi: 10.1016/0304-4076(82)90105-1
  • Escanciano JC. A consistent diagnostic test for regression models using projections. Econ Theory. 2006;22:1030–1051. doi: 10.1017/S0266466606060506
  • Lee T-H, White H, Granger CWJ. Testing for neglected nonlinearity in time series models: a comparison of neural network methods and alternative tests. J Econom. 2001;56:208–229.
  • Lin DY, Wei LJ, Ying Z. Model-checking techniques based on cumulative residuals. Biometrics. 2002;58:1–12. doi: 10.1111/biom.2002.58.issue-1
  • Stute W. Nonparametric model checks for regression. Ann Stat. 1997;25:613–641. doi: 10.1214/aos/1031833666
  • Bierens HJ, Ploberger W. Asymptotic theory of integrated conditional moment tests. Econometrica. 1997;65:1129–1151. doi: 10.2307/2171881
  • Ma S, Zhang J, Sun Z, et al. Integrated conditional moment test for partially linear single index models incorporating dimension-reduction. Electron J Stat. 2014;8(1):523–542. doi: 10.1214/14-EJS893
  • Jones LK. On a conjecture of Huber concerning the convergence of projection pursuit regression. Ann Stat. 1987;15:880–882. doi: 10.1214/aos/1176350382
  • Härdle WK, Mammen E. Comparing nonparametric versus parametric regression fits. Ann Stat. 1993;21(4):1926–1947.
  • Li Q, Wang S. A simple consistent bootstrap test for a parametric regression function. J Econom. 1998;87(1):145–165. doi: 10.1016/S0304-4076(98)00011-6
  • Mammen E. Bootstrap and wild bootstrap for high-dimensional linear models. Ann Statist. 1993;21(1):255–285. doi: 10.1214/aos/1176349025
  • Stute W, González Manteiga W, Presedo Quindimil M. Bootstrap approximations in model checks for regression. J Amer Stat Assoc. 1998;93(441):141–149. doi: 10.1080/01621459.1998.10474096
  • Zhao Y, Xue L, Feng S. Semiparametric estimation of the single-index varying-coefficient model. Commun Stat – Theory Methods. 2017;46:4311–4326. doi: 10.1080/03610926.2015.1081950

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