Inference on a regression model with noised variables and serially correlated errors

doi:10.1016/j.jmva.2008.10.011

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	Inference on a regression model with noised variables and serially correlated errors
	You, Jinhong 2; Zhou, Xian 1; Zhu, Li-Xing 3
刊名	JOURNAL OF MULTIVARIATE ANALYSIS
	2009-07
卷号	100 期号:6 页码:1182-1197
关键词	Regression with noised variables De-noising Serially correlated errors ARMA model Asymptotic normality Consistency
ISSN号	0047-259X
DOI	10.1016/j.jmva.2008.10.011
英文摘要	Motivated by a practical problem, [Z.W. Cai, P.A. Naik, C.L. Tsai, De-noised least squares estimators: An application to estimating advertising effectiveness, Statist. Sinica 10 (2000) 1231-1243] proposed a new regression model with noised variables due to measurement errors. In this model, the means of some covariates are nonparametric functions of an auxiliary variable. They also proposed a de-noised estimator for the parameters of interest, and showed that it is root-n consistent and asymptotically normal when undersmoothing is applied. The undersmoothing, however, causes difficulty in selecting the bandwidth. In this paper, we propose an alternative corrected de-noised estimator, which is asymptotically normal without the need for undersmoothing. The asymptotic normality holds over a fairly wide range of bandwidth. A consistent estimator of the asymptotic covariance matrix under a general stationary error process is also proposed. In addition, we discuss the fitting of the error structure, which is important for modeling diagnostics and statistical inference, and extend the existing error structure fitting method to this new regression model. A simulation study is made to evaluate the proposed estimators, and an application to a set of advertising data is also illustrated. (C) 2008 Elsevier Inc. All rights reserved.
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER INC
WOS记录号	WOS:000265805600008
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2459]
专题	上海财经大学
通讯作者	Zhou, Xian
作者单位	1.Macquarie Univ, Dept Actuarial Studies, Sydney, NSW 2109, Australia; 2.Shanghai Univ Finance & Econ, Shanghai, Peoples R China; 3.Hong Kong Baptist Univ, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	You, Jinhong,Zhou, Xian,Zhu, Li-Xing. Inference on a regression model with noised variables and serially correlated errors[J]. JOURNAL OF MULTIVARIATE ANALYSIS,2009,100(6):1182-1197.
APA	You, Jinhong,Zhou, Xian,&Zhu, Li-Xing.(2009).Inference on a regression model with noised variables and serially correlated errors.JOURNAL OF MULTIVARIATE ANALYSIS,100(6),1182-1197.
MLA	You, Jinhong,et al."Inference on a regression model with noised variables and serially correlated errors".JOURNAL OF MULTIVARIATE ANALYSIS 100.6(2009):1182-1197.