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The focused information criterion for varying-coefficient partially linear measurement error models. (English) Zbl 1371.62038
Summary: Under general parametric models, G. Claeskens and N. L. Hjort [J. Am. Stat. Assoc. 98, No. 464, 900–945 (2003; Zbl 1045.62003)] proposed a focused information criterion for model selection which emphasizes the accuracy of estimation for particular parameters of interest. This paper extends their framework to include a semi-parametric varying-coefficient partially linear model when covariates in both the parametric and the non-parametric parts are subject to measurement errors. We allow the covariance matrices of the measurement errors to be unknown and be estimated by replicated observations. Also, we derive the asymptotic properties of the frequentist model average estimator for the model in consideration, which generalizes the results obtained by the first author et al. [Electron. J. Stat. 6, 1017–1039 (2012; Zbl 1281.62054)]. In addition to asymptotic properties, finite sample performance of the proposed methods are examined in a simulation study, and a data set obtained from Continuing Survey of Food Intakes by Individuals conducted by the U.S. Department of Agriculture’s (CSFII) is considered.

MSC:
62G08 Nonparametric regression and quantile regression
62F12 Asymptotic properties of parametric estimators
62H12 Estimation in multivariate analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
MAMI
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