因变量缺失下部分线性变系数变量含误差模型的估计

Abstract

Abstract:

This paper considers the estimation of partially linear varying-coefficient models, which are useful extensions of varying coefficient models and partially linear models. The author focuses on the case where some covariates are measured with additive errors and the response variable is sometime missing. A class of estimators for the parametric component as well as nonparametric components based on the profile least-squares approach are proposed. The first estimator is constructed by using complete-case observations only, the other two by using simple imputation or replacement techniques respectively to complete the sample. All the proposed estimators for the parametric component are shown to be asymptotically normal, and the estimators of nonparametric component achieve the optimal strong convergence rate of the usual nonparametric regression. For the mean of response variable, two estimators are constructed and their asymptotic normalities are established. Simulation studies are conducted to illustrate the approach.

Key words: Asymptotic normality, Measurement error, Missing data, Partially linear varying-coefficient model, Profile least-squares approach

CLC Number:

62J99

WEI Chuan-Hua. Estimation in Partially Linear Varying-Coefficient Errors-in-Variables Models with Missing Responses[J].Acta mathematica scientia,Series A, 2010, 30(4): 1042-1054.

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References

[1] Hastie T, Tibshirani R. Varying-coefficient models (with discussion). Journal of the Royal Statistical Society, 1993, 55B: 757--796

[2] Engle R F, Granger W J, Rice J, et al. Semiparametric estimates of the relation between weather and electricity sales. J Amer Statist Assoc, 1986, 80: 310--319

[3] Zhang W, Lee S, Song X. Local polynomial fitting in semivarying-coefficient model. J Multivar Anal, 2002, 82: 166--188

[4] Zhou X, You J. Wavelet estimation in varying coefficient partially linear regression models. Statist Probab Lett, 2004, 68: 91--104

[5] Xia Y, Zhang W, Tong H. Efficient estimation for semivarying-coefficient models. Biometrika, 2004, 91: 661--681

[6] Ahmad I, Leelahanon S, Li Q. Efficient estimation of semiparametric partially linear varying coefficient model. Ann Statist, 2005, 33: 258--283

[7] Fan J, Huang T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli, 2005, 11: 1031--1057

[8] You J, Chen G. Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model. J Multivar Anal, 2006, 97: 324--341

[9] Ali M, Abu-Salih M. On estimation of missing observations in linear regression models. Sankhya Indian J Statist, 1988, 50: 404--411

[10] Cheng P. Nonparametric estimation of mean functionals with data missing at random. J Amer Statist Assoc, 1990, 89: 81--87

[11] Chu C, Cheng P. Nonparametric regression estimation with missing data. J Statist Planning Inference, 1995, 48: 85--99

[12] Wang Q, Linton O, Hardle W. Semiparametric regression analysis with missing response at random.J Amer Statist Assoc, 2004, 99: 334--345

[13] Wang Q, Sun Z. Estimation in partially linear models with missing responses at random.J Multivar Anal, 2007, 98: 1470--1493

[14] Little R, Rubin D. Statistical Analysis with Missing Data. New York: John Wiley, 2002

[15] Liang H, Wang S, Carroll R. Partially linear models with missing response variables and error-prone covariates. Biometrika, 2007, 94: 185--198

[16] Mack Y, Silverman B W. Weak and strong uniform consistency of kernel regression estimates. Z Wahrsch Verw Gebiete, 1982, 61: 405--415

[17] Xia Y, Li W. On the estimation and testing of functional-coefficient linear models. Statist Sinica, 1999, 9: 737--757

Estimation in Partially Linear Varying-Coefficient Errors-in-Variables Models with Missing Responses

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