This paper gives a solution to the problem of estimating coefficients of index models, through the estimation of the density-weighted average derivative of a general regression function. The estimators, based on sample analogues of the product moment representation of the average derivative, are constructed using nonparametric kernel estimators of the density of the regressors. Asymptotic normality is established using extensions of classical U-statistic theorems, and asymptotic bias is reduced through use of a higher-order kernel