A method of estimating the average derivative: the multivariate case

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Description/Abstract

The paper uses local linear regression to estimate the ``direct'' Average Derivative \delta = E(D[m(x)]), where m(x) is the regression function. The estimate of \delta is the weighted average of local slope estimates. We prove the asymptotic normality of the estimate under conditions which are different from the conditions used by Heardle-Stoker (H-S) (1989). Using Monte-Carlo simulation experiments we give some small sample results comparing our estimator with the H-S estimator under our conditions for asymptotic normality.