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Optimal minimax rates of specification testing with data-driven bandwidth

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  • Kohtaro Hitomi
  • Masamune Iwasawa
  • Yoshihiko Nishiyama

Abstract

This study investigates optimal minimax rates of specification testing for linear and non-linear instrumental variable regression models. The test constructed by non-parametric kernel techniques can be rate optimal when bandwidths are selected appropriately. Since bandwidths are often selected in a data-dependent way in empirical studies, the rate-optimality of the test with data-driven bandwidths is investigated. While least squares cross-validation selects bandwidths that are optimal for estimation, it is shown not to be optimal for testing. Thus, we propose a novel bandwidth selection method for testing, the performance of which is investigated in a simulation study.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:42:y:2023:i:6:p:487-512
    DOI: 10.1080/07474938.2023.2198929
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    2. 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.

    More about this item

    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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