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Bias-corrected statistical inference for partially linear varying coefficient errors-in-variables models with restricted condition. (English) Zbl 1281.62098
Summary: We consider statistical inference for a partially linear varying coefficient model with measurement errors in the nonparametric part when some prior information about the parametric part is available. The prior information is expressed in the form of exact linear restrictions. Two types of local bias-corrected restricted profile least squares estimators of the parametric component and nonparametric component are conducted, and their asymptotic properties are also studied under some regularity conditions. Moreover, we compare the efficiency of the two kinds of parameter estimators under the criterion of Löwner ordering. Finally, we develop a linear hypothesis test for the parametric component. Some simulation studies are conducted to examine the finite sample performance for the proposed method. A real data set is analyzed for illustration.

MSC:
62G08 Nonparametric regression and quantile regression
62F10 Point estimation
62F30 Parametric inference under constraints
60E15 Inequalities; stochastic orderings
62J05 Linear regression; mixed models
65C60 Computational problems in statistics (MSC2010)
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