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Local rank estimation and related test for varying-coefficient partially linear models. (English) Zbl 1359.62111
Summary: This paper develops a robust estimation procedure for the varying-coefficient partially linear model via local rank technique. The new procedure provides a highly efficient and robust alternative to the local linear least-squares method. In other words, the proposed method is highly efficient across a wide class of non-normal error distributions and it only loses a small amount of efficiency for normal error. Moreover, a test for the hypothesis of constancy for the nonparametric component is proposed. The test statistic is simple and thus the test procedure can be easily implemented. We conduct Monte Carlo simulation to examine the finite sample performance of the proposed procedures and apply them to analyse the environment data set. Both the theoretical and the numerical results demonstrate that the performance of our approach is at least comparable to those existing competitors.

MSC:
62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62G35 Nonparametric robustness
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
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