Abstract
In this paper, we consider the statistical inference for the partially liner varying coefficient model with measurement error 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 Loẅner 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 dataset is analyzed for illustration.
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Acknowledgments
Sanying Feng’s research was supported by the National Nature Science Foundation of China (11101014, 11001118), the National Social Science Foundation of China (11CTJ004) and the Fundamental Research Foundation of Beijing University of Technology (X4006013201101). Liugen Xue’s research was supported by the National Nature Science Foundation of China (11171012), the Science and Technology Project of the Faculty Adviser of Excellent PhD Degree Thesis of Beijing (20111000503) and the Beijing Municipal Education Commission Foundation (KM201110005029).
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Feng, S., Xue, L. Bias-corrected statistical inference for partially linear varying coefficient errors-in-variables models with restricted condition. Ann Inst Stat Math 66, 121–140 (2014). https://doi.org/10.1007/s10463-013-0407-z
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DOI: https://doi.org/10.1007/s10463-013-0407-z