Acta mathematica scientia, Series B >
STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS
Received date: 2006-12-29
Revised date: 2008-09-10
Online published: 2009-09-20
Supported by
Zhou's research was supported by the National Natural Science Funds for Distinguished Young Scholar (70825004) and National Natural Science Foundation of China (NSFC) (10731010 and 10628104), the National Basic Research Program (2007CB814902), Creative Research Groups of China (10721101) and Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics and 211 Project for Shanghai University of Finance and Economics (the 3rd phase)
This article is concerned with the estimating problem of semiparametric varying-coefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang (2005) proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.
Zhou Yong , You Jinhong , Wang Xiaojing . STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1113 -1127 . DOI: 10.1016/S0252-9602(09)60090-4
[1] Brumback B, Rice J A. Smoothing spline models for the analysis of nested and crossed samples of curves (with discussion). J Amer Statist Assoc, 1998, 93: 961--994
[2] Carroll R J, Ruppert D, Welesh A H. Nonparametric estimation via local estimating equations. J Amer Statist Assoc, 1998, 93: 214--227
[3] Chen H, Shiau J. Data-driven efficient estimation for a partially linear model. Ann Statist, 1994, 22: 211--237
[4] Chen R, Tsay R. Functional-coefficient autoregressive models. J Amer Statist Assoc, 1993, 88: 298--308
[5] Donald S G, Newey W K. Series estimation of semilinear models. J Multivariate Anal, 1994, 50: 30--40
[6] Engle R F, Granger W J, Rice J, Weiss A. Semiparametric estimates of the relation between weather and electricity sales. J Amer Statist Assoc, 1986, 80: 310--319
[7] Eubank R, Speckman P. Trigonometric series regression estimators with an application to partially linear models. J Multivariate Anal, 1993, 32: 70--84
[8] Fan J, H\"ardle W, Mammen E. Direct estimation of low-dimensional components in additive models. Ann Statist, 1998, 26: 943--971
[9] Fan J, Huang T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli, 2005, 11: 1031--1057
[10] Fan J, Zhang C, Zhang J. Generalized likelihood ratio statistics and Wilks phenomenon. Ann Statist, 2001, 29: 153--193
[11] Fan J, Zhang W. Statistical estimation in varying coefficient models. Ann Statist, 1999, 27: 1491--1518
[12] Gao J. The laws of the iterated logarithm of some estimates in partly linear models. Statist Probab Lett, 1995, 25: 153--162
[13] Hamilton A, Truong K. Local linear estimation in partly linear models. J Multivariate Anal, 1997, 60: 1--19
[14] Hardle W, Liang H, Gao J T. Partially linear models. Heidelberg: Physica-Verlag, 2000
[15] Hastie T J, Tibshirani R. Varying-coefficient models. J Roy Statist Soc B, 1993, 55: 757--796
[16] Hoover D R, Rice J A, Wu C O, Yang L P. Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, 1998, 85: 809--822
[17] Huang J Z, Wu C O, Zhou L. Varying-coefficient model and biasis function approximations for the analysis of repeated measurements. Biometrika, 2002, 89: 809--822
[18] Lai T L, Robbins H, Wei C Z. Strong consistency of least squares estimates in multiple regression II. J Mulutivariate Anal, 1979, 9: 343--361
[19] Li Q, Huang C J, Li D, Fu T T. Semiparametric smooth coefficient models. J Business and Econ Statist, 2002, 3: 412--422
[20] Liang H, H\"ardle W, Carroll R J. Estimation in a semiparametric partially linear errors-in-variables model. Ann Statist, 1999, 27: 1519--1535
[21] Park M G, Sun J. Tests in projection pursuit regression. J Statist Plann Inference, 1998, 75: 65--90
[22] Robinson P. Root-N-consistent semiparametric regression. Econometrica, 1988, 56: 931--954
[23] Severini T A, Staniswalis J G. Quasilikehood estimation in semiparametric models. J Amer Statist Assoc, 1994, 90: 501--511
[24] Shi P, Li G. A note of the convergence rates of M-estimates for partially linear model. Statistics, 1995, 26: 27--47
[25] Speckman P. Kernel smoothing in partial linear models. J Roy Statist Soc B, 1988, 50: 413--436
[26] Stone C J. Optimal global rates of convergence for nonparametric regression. Ann Statist, 1982, 10: 1040--1053
[27] Stout W F. Almost Sure Convergence. New York: Academic Press, 1974
[28] Xia Y, Li W K. On the estimation and testing of functional-coefficient linear models. Statistica Sinica, 1999, 9: 737--757
[29] Wu C O, Chiang C T, Hoover D R. Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data.
J Amer Statist Assoc, 1998, 93: 1388--1402
[30] Zhang W, Lee S Y, Song X. Local polynomial fitting in semivarying coefficient models. J Multivariate Anal, 2002, 82: 166--188
[31] Zhu L, Fang K. Asymptotics for kernel estimate of sliced inverse regression. Ann Statist, 1996, 24: 1053--1068
/
| 〈 |
|
〉 |