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Optimal Minimax Rates against Non-smooth Alternatives

Kohtaro Hitomi (), Masamune Iwasawa () and Yoshihiko Nishiyama ()
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Kohtaro Hitomi: Kyoto Institute of Technology
Yoshihiko Nishiyama: Institute of Economic Research, Kyoto University

No 1051, KIER Working Papers from Kyoto University, Institute of Economic Research

Abstract: This study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of non-smooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is n−1/4, where n is the sample size. The rate is achieved by a simple test based on the difference between non-parametric and parametric variance estimators.

Keywords: optimal minimax rate; specification test; instrumental variable regression model; nearest neighbor method (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2020-12
New Economics Papers: this item is included in nep-ecm and nep-ore
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