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Uniform bahadur representation for local polynomial estimates of M-regression and its application to the additive model

By Efang Kong, Oliver Linton and Yingcun Xia


We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Y-i, (X) under bar (i))}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We apply our results to the estimation of an additive M-regression model

Topics: QA Mathematics
Publisher: Cambridge University Press
Year: 2010
DOI identifier: 10.1017/S0266466609990661
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Provided by: LSE Research Online
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