OPTIMAL MINIMAX RATES FOR NONPARAMETRIC SPECIFICATION TESTING IN REGRESSION MODELS
研究了在非线性参数回归函数设定检验中，采用非参数极小化最大方法确定光滑备择假设趋近原假设的最大速率，并证明光滑非参数检验具有最优渐近性质，而一类非光滑检验（如Bierens积分条件矩检验）则次优。
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.