Abstract
We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n −1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n −1/2-rate.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Robins, J., Li, L., Tchetgen, E. et al. Quadratic semiparametric Von Mises calculus. Metrika 69, 227–247 (2009). https://doi.org/10.1007/s00184-008-0214-3
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DOI: https://doi.org/10.1007/s00184-008-0214-3