Optimal minimax rates against nonsmooth alternatives

Optimal testing for additivity in multiple nonparametric regression

Kohtaro Hitomi, Masamune Iwasawa and Yoshihiko Nishiyama

The Econometrics Journal, 2022, vol. 25, issue 2, 322-339

Abstract: SummaryThis study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of nonsmooth 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 , where n is the sample size. The rate is achieved by a simple test based on the difference between nonparametric and parametric variance estimators. Simulation studies illustrate that the test has reasonable power against various nonsmooth alternatives. The empirical application to Engel curves specification emphasizes the good applicability of the test.

Keywords: Optimal minimax rate; specification test; instrumental variable regression model; nearest neighbour method (search for similar items in EconPapers)
Date: 2022
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Working Paper: Optimal Minimax Rates against Non-smooth Alternatives (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:oup:emjrnl:v:25:y:2022:i:2:p:322-339.

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