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Optimal minimax rates against nonsmooth alternatives
[Optimal testing for additivity in multiple nonparametric regression]

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  • Kohtaro Hitomi
  • Masamune Iwasawa
  • Yoshihiko Nishiyama

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.

Suggested Citation

  • Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2022. "Optimal minimax rates against nonsmooth alternatives [Optimal testing for additivity in multiple nonparametric regression]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 322-339.
    • Handle: RePEc:oup:emjrnl:v:25:y:2022:i:2:p:322-339.
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    File URL: http://hdl.handle.net/10.1093/ectj/utab030
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    1. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2023. "Optimal minimax rates of specification testing with data-driven bandwidth," Econometric Reviews, Taylor & Francis Journals, vol. 42(6), pages 487-512, June.

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    More about this item

    Keywords

    Optimal minimax rate; specification test; instrumental variable regression model; nearest neighbour method;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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