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Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model. (English) Zbl 1085.62043
Summary: This paper studies the estimation of a varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model of J. Fan and T. Huang [Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Manuscript, Univ. North Carolina, Chapel Hill, USA (2002)]. We focus on the case where some covariates are measured with additive errors. The usual profile least squares and local polynomial estimations lead to biased estimators of the parametric and nonparametric components, respectively, when measurement errors are ignored. By correcting the attenuation we propose a modified profile least squares estimator for the parametric component and a local polynomial estimator for the nonparametric component. We show that the former is consistent, asymptotically normal and achieves the rate in the law of the iterated logarithm, and the latter achieves the optimal strong convergence rate of the usual nonparametric regression. In addition, a consistent estimator is also developed for the error variance. These results can be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.
62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency
62H12Multivariate estimation