Optimal minimax rates of specification testing with data-driven bandwidth

Kohtaro Hitomi, Masamune Iwasawa and Yoshihiko Nishiyama

Econometric Reviews, 2023, vol. 42, issue 6, 487-512

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.

Date: 2023
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Working Paper: Optimal Minimax Rates of Specification Testing with Data-driven Bandwidth (2021)
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DOI: 10.1080/07474938.2023.2198929

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