In the context of testing the specification of a nonlinear parametric regression function, we adopt a nonparametric minimax approach to determine the maximum rate at which a set of smooth alternatives can approach the null hypothesis while ensuring that a test can uniformly detect any alternative in this set with some predetermined power. We show that a smooth nonparametric test has optimal asymptotic minimax properties for regular alternatives. As a by-product, we obtain the rate of the smoothing parameter that ensures rate-optimality of the test. We show that, in contrast, a class of nonsmooth tests, which includes the integrated conditional moment test of Bierens (1982, Journal of Econometrics 20, 105 134), has suboptimal asymptotic minimax properties.
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Article provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 18 (2002) Issue (Month): 05 (October) Pages: 1139-1171 Download reference. The following formats are available: HTML
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