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We consider nonparametric estimation of an object such as a probability density or a regression function. Can such an estimator achieve the minimax rate of convergence on suitable function spaces, while, at the same time, when ``plugged-in'', estimate efficiently (at a rate of $n^(-1/2)$ with the best constant) many functionals of the object? For example, can we have a density estimator whose definite integrals are efficient estimators of the cumulative distribution function? We show that this is impossible for very large sets, e.g., expectations of all functions bounded by $M<\en$. However we also show that it is possible for sets as large as indicators of all quadrants, i.e., distribution functions. We give appropriate constructions of such estimates.

Details

Title
Non-Parametric Estimators Which Can Be ``Plugged-In''
Creator
Bickel, Peter J., Author
Ritov, Ya'acov, Author
Published
Statistics Department, University of California, Berkeley, University of California at Berkeley, Berkeley, California, Jul 2001
Full Collection Name
Statistics Technical Reports
Other Identifiers
602
Type
Text
Format
technical reports
Archive
Mathematics Statistics Library
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