ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

doi:10.1016/S0252-9602(10)60069-0

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 677-687.doi: 10.1016/S0252-9602(10)60069-0

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

田萍, 杨林, 薛留根

Department of Mathematics, Xuchang University, Xuchang 461000, China|College of Applied Sciences, Beijing University of Technology, Beijing 100022, China

收稿日期:2006-05-18 修回日期:2008-08-27 出版日期:2010-05-20 发布日期:2010-05-20
基金资助:
Supported by the National Natural Science Foundation of China (10571008), the Natural Science Foundation of Henan (092300410149), and the Core Teacher Foundation of Henan (2006141)

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

TIAN Ping, YANG Lin, XUE Liu-Gen

Department of Mathematics, Xuchang University, Xuchang 461000, China|College of Applied Sciences, Beijing University of Technology, Beijing 100022, China

Received:2006-05-18 Revised:2008-08-27 Online:2010-05-20 Published:2010-05-20
Supported by:
Supported by the National Natural Science Foundation of China (10571008),
the Natural Science Foundation of Henan (092300410149), and the Core Teacher Foundation of Henan (2006141)

摘要/Abstract

摘要：

In this article, a partially linear single-index model for longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.

关键词: Longitudinal data, partially linear single-index model, penalized spline, strong consistency, asymptotic normality

Abstract:

Key words: Longitudinal data, partially linear single-index model, penalized spline, strong consistency, asymptotic normality

中图分类号:

62G05

田萍, 杨林, 薛留根. ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA[J]. 数学物理学报(英文版), 2010, 30(3): 677-687.

TIAN Ping, YANG Lin, XUE Liu-Gen. ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA[J]. Acta mathematica scientia,Series B, 2010, 30(3): 677-687.

参考文献

[1] Stoker T M. Consistint estimation of scaled coefficients. Econometrica, 1986, 54(6): 1461--1481

[2] Härdle W, Stocker T M. Investigating smooth multiple regression by the method of average derivatives. Journal of the American Statistical Association, 1989, 84(408): 986--995

[3] Ichimura H. Semiparametric least squares(SLS) and weighted SLS estimation of single-index models.
Journal of Econometrics, 1993, 58: 71--120

[4] Härdle W, Hall P, Ichimura H. Optimal smoothing in single-index models. The Annals of Statistics, 1993, 21(1): 157--178

[5] Yu Y, Ruppert D. Penalized spline estimation for partially linear single index models. Journal of the American Statistical Association, 2002, 97(460): 1042--1054

[6] Yu Y, Ruppert D. Root-n consistency of Penalized spline estimation for partially linear single index models under general euclidean space. Statistica Sinica, 2004, 14: 449--455

[7] Carroll R J, Fan J, Gijbels I, et al. Generalized partially linear single-index models. Journal of the American Statistical Association, 1997, 92(438): 477--489

[8] Delecroix M, H\"ardle W, Hristache M. Efficient estimation in conditional single-index regression. Journal of Multivariate Analysis, 2003, 86: 213--226

[9] Xue L G, Zhu L X. Empirical likelihood confidence regions of the parameters in a partially linear single-index model. Science in China Ser.A(in Chinese), 2005, 48(10): 1333--1348

[10] Diggle P J, Heagerty P J, Liang K Y. Analysis of Longitudinal Data. New York: Oxford University Press Inc., 2002. 1--1

[11] Lin Z Y, Lu C R, Su Z G. Foundations of the Theory of Probalility Limits (in Chinese). Beijing: Higher Education Press, 1999: 95--95

[12] Chen M H. Consistency of a class of estimators in semiparametric regression model under fixed design.
Applied Mathematics A Journal of Chinese Universities(in Chinese), 1998, 13(3): 301--310

[13] Jennrich R I. Asymptotic properties of nonlinear least squares estimators. The Annals of Mathematical Statistics, 1969, 40(2): 633--643

[14] Wu C F. Asymptotic theory of nonlinear least squares estimation. The Annals of Statistics, 1981, 9(3): 501--513

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

Metrics

本文评价

推荐阅读 0

[1]	刘美琪, 乔会杰. PARAMETER ESTIMATION OF PATH-DEPENDENT MCKEAN-VLASOV STOCHASTIC DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2022, 42(3): 876-886.
[2]	童行伟, 胡涛, 崔恒建. HAZARD REGRESSION WITH PENALIZED SPLINE: THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS[J]. 数学物理学报(英文版), 2010, 30(5): 1759-1768.
[3]	刘妍岩, 张艳丽. THE CONSISTENCY AND ASYMPTOTIC NORMALITY OF NEAREST NEIGHBOR DENSITY ESTIMATOR UNDER α- \|MIXING CONDITION[J]. 数学物理学报(英文版), 2010, 30(3): 733-738.
[4]	缪柏其, 吴月华, 刘东海. LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES[J]. 数学物理学报(英文版), 2010, 30(1): 319-329.
[5]	张日权; 李国英. EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES[J]. 数学物理学报(英文版), 2008, 28(4): 989-997.
[6]	秦国友; 朱仲义. ROBUST ESTIMATION IN PARTIAL LINEAR MIXED MODEL FOR LONGITUDINAL DATA[J]. 数学物理学报(英文版), 2008, 28(2): 333-347.
[7]	陈清平, 戴永隆. KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA[J]. 数学物理学报(英文版), 2003, 23(4): 477-.
[8]	张三国, 陈希孺. ASYMPTOTIC NORMALITY OF PARAMETERS ESTIMATION IN EV MODEL WITH REPLICATED OBSERVATIONS[J]. 数学物理学报(英文版), 2002, 22(1): 107-114.
[9]	胡舒合, 朱春华, 程业斌, 王立春. FIXED-DESIGN REGRESSION FOR LINEAR TIME SERIES[J]. 数学物理学报(英文版), 2002, 22(1): 9-18.
[10]	白志东, 陈桂景, 胡飞芳. A KIND OF URN MODEL FOR ADAPTIVE SEQUENTIAL DESIGN[J]. 数学物理学报(英文版), 2001, 21(2): 224-228.
[11]	胡舒合. SEMIPARAMETRIC REGRESSION MODELS WITH LOCALLY GENERALIZED GAUSSIAN ERROR'S STRUCTURE[J]. 数学物理学报(英文版), 1998, 18(S1): 68-77.
[12]	王启华. SOME LARGE SAMPLE PROPERTIES OF AN ESTIMATOR OF THE HAZARD FUNCTION FROM RANDOMLY CENSORED DATA[J]. 数学物理学报(英文版), 1997, 17(2): 230-240.
[13]	秦更生, 蔡雷. ESTIMATION FOR THE AYMPTOTIC VARIANCE OF PARAMETRIC ESTIMATES IN PARTIAL LINEAR MODEL WITH CENSORED DATA[J]. 数学物理学报(英文版), 1996, 16(2): 192-208.
[14]	周勇. A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA[J]. 数学物理学报(英文版), 1996, 16(2): 170-180.