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Nonparametric estimation when data on derivatives are available

Hall, Peter; Yatchew, Adonis


We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when derivative data are available, local averages can be replaced in certain dimensions by nonlocal averages, thus reducing the nonparametric dimension of the problem. We derive optimal rates of convergence and conditions under which dimension reduction is...[Show more]

CollectionsANU Research Publications
Date published: 2007-08-03
Type: Journal article
Source: Annals of Statistics
DOI: 10.1214/009053606000001127


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