Uniform Bahadur Representation for Local Polynomial Estimates of M-Regression and Its Application to The Additive Model

Details Uniform Bahadur Representation for Local Polynomial Estimates of M-Regression and Its Application to The Additive Model Uniform Bahadur Representation for Local Polynomial Estimates of M-Regression and Its Application to The Additive Model

2007-09-11

arxiv.org/abs/0709.1663v2

Mathematics

Statistics Theory

40 pages

Scientific paper

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes $\{(Y_{i},\underline{X}_{i})\}$. 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 in such estimators into other functionals where some control over higher order terms are required. We apply our results to the estimation of an additive M-regression model.

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