UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL

Efang Kong, Oliver Linton and Yingcun Xia

Econometric Theory, 2010, vol. 26, issue 5, 1529-1564

Abstract: We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Yi, Xi)}. 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.

Date: 2010
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Working Paper: Uniform Bahadur Representation for LocalPolynomial Estimates of M-Regressionand Its Application to The Additive Model (2009)
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