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# Nonparametric Hypothesis Testing with Parametric Rates of Convergence

Paul Rilstone
International Economic Review
Vol. 32, No. 1 (Feb., 1991), pp. 209-227
DOI: 10.2307/2526941
Stable URL: http://www.jstor.org/stable/2526941
Page Count: 19
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## Abstract

Nonparametric estimators are frequently criticized for their poor performance in small samples. In this paper we consider using kernel methods for the estimation of the expected derivatives of a regression function. The proposed estimators are shown to be asymptotically normal and $\sqrt{n}$-consistent. As a consequence their standard errors are comparable to parametric estimates. An empirical example demonstrates the facility of the approach.

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