UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL
研究了强混合平稳过程中M回归函数的局部多项式估计，建立了回归函数及其导数估计的Bahadur表示的一致强收敛速度，并将结果应用于可加M回归模型的估计。
We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {( Y i , 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 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.