Multivariate Local Polynomial Kernel Estimators: Leading Bias and Asymptotic Distribution∗

Masry (1996b) provides estimation bias and variance expression for a general local polynomial kernel estimator in a general multivariate regression framework. Under smoother conditions on the unknown regression and by including more rened approximation terms than that in Masry (1996b), we extend the result of Masry (1996b) to obtain explicit leading bias terms for the whole vector of the local poly-nomial estimator. Specically, we derive the leading bias and leading variance terms of nonparametric local polynomial kernel estimator in a general nonparametric multivariate regression model framework. The results can be used to obtain optimal smoothing parameters in local polynomial estimation of the unknown conditional mean function and its derivative functions.