Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24680
Title: Statistical inference on semi-parametric partial linear additive models
Authors: Wei, CH
Liu, C 
Keywords: backfitting
generalised likelihood ratio test
partial linear additive models
profile least-squares
restricted estimation
Issue Date: 2012
Publisher: Taylor & Francis Ltd
Source: Journal of nonparametric statistics, 2012, v. 24, no. 4, p. 809-823 How to cite?
Journal: Journal of Nonparametric Statistics 
Abstract: In the framework of partial linear additive models, we first develop a profile least-squares estimation of the parametric component based on Liang et al.'s [(2008), 'Additive Partial Linear Models with Measurement Errors', Biometrika, 95(3), 667-678] work. This estimator is shown to be asymptotically normal and root-n consistent without requirement of undersmoothing of the nonparametric component. Next, when some additional linear restrictions on the parametric component are available, we postulate a restricted profile least-squares estimator for the parametric component and prove the asymptotic normality of the resulting estimator. To check the validity of the linear constraints on the parametric component, we explore a generalised likelihood ratio test statistic and demonstrate that it follows asymptotically chi-squared distribution under the null hypothesis. Thus, the result unveils a new Wilks type of phenomenon. Simulation studies are conducted to illustrate the proposed methods. An application to the crime rate data in Columbus (Ohio) has been carried out.
URI: http://hdl.handle.net/10397/24680
DOI: 10.1080/10485252.2012.716155
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