The influence function of semiparametric estimators

Hidehiko Ichimura and Whitney Newey

No CWP44/15, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: Often semiparametric estimators are asymptotically equivalent to a sample average. The object being averaged is referred to as the in?uence function. The in?uence function is useful in formulating primitive regularity conditions for asymptotic normality, in efficiency comparions, for bias reduction, and for analyzing robustness. We show that the in?uence function of a semiparametric estimator can be calculated as the limit of the Gateaux derivative of a parameter with respect to a smooth deviation as the deviation approaches a point mass. We also consider high level and primitive regularity conditions for validity of the in?uence function calculation. The conditions involve Frechet differentiability, nonparametric convergence rates, stochastic equicontinuity, and small bias conditions. We apply these results to examples.

Date: 2015-08-07
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Citations: View citations in EconPapers (13)

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Working Paper: The influence function of semiparametric estimators (2015)
Working Paper: The Influence Function of Semiparametric Estimators (2015)
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