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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.
Authors
Research Associate University of Arizona, University of Tokyo
Hidehiko is a Professor of Economics at the Eller College of Management, University of Arizona and a Research Associate at the IFS.
Whitney K. Newey
Working Paper details
- DOI
- 10.1920/wp.cem.2015.4415
- Publisher
- cemmap
Suggested citation
Ichimura, H and Newey, W. (2015). The influence function of semiparametric estimators. London: cemmap. Available at: https://ifs.org.uk/publications/influence-function-semiparametric-estimators (accessed: 9 May 2024).
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