Multivariate local polynomial regression for estimating average derivatives

Abstract

In this paper we suggest to use the sample average of the derivative estimators from a local polynomial fitting to estimate the average derivatives of an unknown multivariate function. Using the techniques of Masry (1996a Masry, E. (1996a). Multivariate regression estimation local polynomial fitting for time series. Stochastic Processes and Their Applications, 65: 81–101. [Crossref], [Web of Science ®] , [Google Scholar],b) Masry, E. (1996b). Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis, 17: 571–599. [Crossref] , [Google Scholar], we derive the asymptotic normal distribution of the proposed average derivative estimator. Monte Carlo experiments show that the proposed estimator compares well with the existing estimators.