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The influence function of semiparametric estimators

Authors: Hidehiko Ichimura and Whitney K. Newey
Date: 07 August 2015
Type: cemmap Working Paper, CWP44/15
DOI: 10.1920/wp.cem.2015.4415


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 comparions, 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.

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Hidehiko Ichimura and Whitney K. Newey January 2017, The influence function of semiparametric estimators, cemmap Working Paper, The IFS

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