Estimation and Inference for Generalized Full and Partial Means and Average Derivatives

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Abstract:

We propose new semiparametric estimators for parameters that depend on the derivatives (up to any finite order) of unknown conditional expectations and densities. We consider two cases. In the first we average over all (conditioning) variables in the conditional expectation or density. In the second case we average over a strict subset of the conditioning variables. The unknown conditional expectations and densities are estimated by a first step kernel estimator. The kernel estimator has a boundary correction that makes it uniformly consistent if the distribution of the covariates has bounded support. The partial and full mean estimators therefore do not require trimming (asymptotic or fixed) as in the estimators developed by Newey (1994) and Powell, Stock, and Stoker (1989) and in many applications to specific settings. We provide a general formula for the influence function and the asymptotic variance for both full and partial averaging. We also specify a general set of regularity conditions that contains a new restriction on the kernel function to avoid bias in the case that the parameter depends on the derivatives of the conditional expectation or density.

Last updated on 07/06/2012