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A Journal of Theoretical and Applied Statistics
Volume 54, 2020 - Issue 6
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Research Article

Asymptotic properties for the estimators in heteroscedastic semiparametric EV models with α-mixing errors

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Pages 1232-1254 | Received 04 Jun 2020, Accepted 17 Dec 2020, Published online: 06 Jan 2021

References

  • Gao JT, Chen XR, Zhao LC. Asymptotic normality of a class of estimators in partial linear models. Acta Math Sinica Chinese Ser. 1994;37(2):256–268.
  • Chen MH, Ren Z, Hu SH. Strong consistency of a class of estimators in partial linear model. Acta Math Sinica Chinese Ser. 1998;41(2):429–439.
  • Baek J, Liang H. Asymptotics of estimators in semiparametric model under NA samples. J Stat Plan Inference. 2006;136:3362–3382.
  • Zhou XC, Hu SH. Moment consistency of estimators in semiparametric regression model under NA samples. Pure Appl Math. 2010;26(2):262–269.
  • Liang HY, Mammitzsch V, Steinebach J. On a semiparametric regression model whose errors form a linear process with negatively associated innovations. Stat: A J Theor Appl Statist. 2006;40(3):207–226.
  • Nkou EDD, Nkiet GM. Strong consistency of kernel estimator in a semiparametric regression model. Statist: A J Theor Appl Statis. 2019;53(6):1289–1305.
  • Wang XJ, Deng X, Hu SH. On consistency of the weighted least squares estimators in a semiparametric regression model. Metrika. 2018;81:797–820.
  • Zhang JJ, Liang HY. Berry-Esseen type bounds in heteroscedastic semi-parametric model. J Stat Plan Inference. 2011;141:3447–3462.
  • Zhang JJ, Liang HY. Asymptotic normality of estimators in heteroscedastic semi-parametric model with strong mixing errors. Commun Statist-Theory Methods. 2012;41(12):2172–2201.
  • Zhou XC, Lin JG. Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors. J Multivar Anal. 2013;122:251–270.
  • Engle RF, Granger CWJ, Riice J, et al. Semiparametric estimates of the relation between weather and electricity sales. J Am Stat Assoc. 1986;81(394):310–320.
  • Hu SH. Estimate for a semiparametric regression model. Acta Math Sci Ser A. 1999;19(5):541–549.
  • Härdle W, Liang H, Gao JT. Partial linear models. Heidelberg: Physica-Verlag; 2000.
  • Shi J, Lau TS. Empirical likelihood for partially linear models. J Multivar Anal. 2000;72(1):132–148.
  • Pan GM, Hu SH, Fang LB, et al. Mean consistency for a semiparametric regression model. Acta Math Sci Ser A. 2003;23(5):598–606.
  • Hu SH. Fixed-design semiparametric regression for linear time series. Acta Math Sci Ser B. 2006;26(1):74–82.
  • Liang H. Generalized partially linear models with missing covariates. J Multivar Anal. 2008;99(5):880–895.
  • Wang LL, Xue L, Qu A, et al. Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates. Ann Statist. 2014;42(2):592–624.
  • Reiersøl O. Identification of a linear relation between variable which are subject to error. Econometrica. 1950;18:375–389.
  • Deaton A. Panel data from time series of cross-sections. J Econom. 1985;30:109–126.
  • Fuller WA. Measurement error models. New York: Wiley; 1987.
  • Carroll RJ, Ruppert D, Stefanski LA. Measurement error in nonlinear models. London: Chapman Hall; 1995.
  • Miao Y, Wang K, Zhao FF. Some limit behaviors for the LS estimator in simple linear EV regression models. Statist Probab Lett. 2011;81(1):92–102.
  • Wang XJ, Shen AT, Chen ZY, et al. Complete convergence for weighted sums of NSD random variables and its application in the EV regression model. TEST. 2015;24(1):166–184.
  • Hu D, Chen PY, Sung SH. Strong laws for weighted sums of ψ-mixing random variables and applications in errors-in-variables regression models. TEST. 2017;26(3):600–617.
  • Chen PY, Kong NN, Sung SH. Complete convergence for weighted sums of i.i.d. random variables with applications in regression estimation and EV model. Commun Statist-Theory Methods. 2017;46(7):3599–3613.
  • Zhang MY, Chen PY, Sung SH. Convergence rates in the weak law of large numbers for weighted sums of i.i.d random variables and applications in errors-in-variables models. Stoch Dyn. 2019;19(2). Article ID 1950041, 13 pages.
  • Cui HJ, Li RC. On parameter estimation for semi-linear errors-in-variables models. J Multivar Anal. 1998;64(1):1–24.
  • Wang QH. Estimation of partial linear errors-in-variables models with validation data. J Multivar Anal. 1999;69(1):30–64.
  • Zhou HB, You JH, Zhou B. Statistical inference for fixed-effects partially linear regression models with errors in variables. Stat Papers. 2010;51(3):629–650.
  • Zhang JJ, Liang HY, Amei A. Asymptotic normality of estimators in heteroscedastic errors-in-variables model. AStA-Adv Statist Anal. 2014;98(2):165–195.
  • Zhang JJ, Wang T. Strong consistency rate of estimators in heteroscedastic errors-in-variables model for negative association samples. Filomat. 2018;32(13):4639–4654.
  • Liang H, Hardle W, Carrol RJ. Estimation in a semiparametric partially linear errosr-in-variables model. Ann Statist. 1999;27(5):1519–1535.
  • Rosenblatt M. A central limit theorem and a strong mixing condition. Proc National Acad Sci USA. 1956;42(1):43–47. doi:10.1073/pnas.42.1.43.
  • Bradley RC. Basic properties of strong mixing conditions. A survey and some open questions. Probab. Surveys. 2005;2:107–144.
  • Davis RA, Mikosch T. The sample autocorrelations of heavy-tailed process with applications to ARCH. Ann Statist. 1998;26(5):2049–2080.
  • Doukhan P. Mixing properties and examples. Berlin: Springer; 1994. (Lecture Notes in Statistics; vol. 85).
  • Fan JQ, Yao QW. Nonlinear time series: nonparametric and parametric methods. New York: Springer; 2006. (Springer Series in Statistics).
  • Liang HY, Jing BY. Asymptotic normality in partial linear models based on dependent errors. J Stat Plan Inference. 2009;139(4):1357–1371.
  • Shao QM. Complete convergence for α-mixing sequences. Statist Probab Lett. 1993;16(4):279–287.
  • Yang SC. Maximal moment inequality for partial sums of strong mixing sequences and application. Acta Math Sin Engl Ser. 2007;23(6):1013–1024.
  • Liebscher E. Estimation of the density and the regression function under mixing conditions. Statist Risk Model Appl Finance Insurance. 2001;19(1):9–26.

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