The Influence Function of Semiparametric Estimators

Hidehiko Ichimura and Whitney Newey

No CIRJE-F-985, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: Often semiparametric estimators are asymptotically equivalent to a sample average. The object being averaged is referred to as the influence function. The influence function is useful in formulating primitive regularity conditions for asymptotic normality, in efficiency comparisons, for bias reduction, and for analyzing robustness. We show that the influence 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 influence function calculation. The conditions involve Frechet differentiability, nonparametric convergence rates, stochastic equicontinuity, and small bias conditions. We apply these results to examples. --

Pages: 27 pages
Date: 2015-08
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Citations: View citations in EconPapers (13)

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Related works:
Journal Article: The influence function of semiparametric estimators (2022)
Working Paper: The influence function of semiparametric estimators (2017)
Working Paper: The influence function of semiparametric estimators (2017)
Working Paper: The influence function of semiparametric estimators (2015)
Working Paper: The influence function of semiparametric estimators (2015)
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