Medizinische Universität Graz Austria/Österreich - Forschungsportal - Medical University of Graz

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Gewählte Publikation:

Schimek, MG.
Estimation and inference in partially linear models with smoothing splines
J STATIST PLAN INFER 2000 91: 525-540. Doi: 10.1016/S0378-3758(00)00197-X
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Führende Autor*innen der Med Uni Graz: Schimek Michael
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Abstract:: A new estimation concept for partially linear models based on smoothing splines has been recently introduced in Eubank et al. (Comput. Statist. Data Anal. 29 (1998) 27). It is based on Speckman's (J. Roy. Statist. Sec. Ser. B 50 (1988) 413) approach. Here, we describe cheap direct algorithms for this approach as well as for the well-Known approach of Green et al. (J. Roy. Statist. Sec. Ser. B 47 (1985) 294). The smoothing parameter can be selected via an unbiased risk criterion. This requires the estimation of the model variance and the evaluation of the hat matrix. Standard errors of the parametric coefficients can be obtained from the estimated covariance matrix. Inference is discussed for both the parametric and the nonparametric part of the model. The time demand of all algorithms is only linear. They can be executed from the statistical and graphical environment S-Plus. Under correlation between the parametric and the nonparametric part of the model, which is quite common in practice, the approach due to Green et al. (1985) is known to be asymptotically biased. Apart from the bias, correlation can cause estimation problems. Hence we study and compare the small sample performance of both approaches. For this purpose a simulation study is performed. We find that both approaches work well for reasonable signal-to-noise ratios and sample sizes, even under correlation. But for inferential purposes we suggest to use the Speckman estimates. (C) 2000 Elsevier Science B.V. All rights reserved.
Find related publications in this database (Keywords): algorithms; asymptotic bias; correlation; partially linear model; semiparametric regression; simulations; smoothing spline; S-Plus; unbiased risk