Minimax Rates for Nonparametric Specification Testing in Regression Models
We deal with the issue of testing the specification of a regression function. As a leading case, we consider testing for a pure noise model. We study the smallest local alternatives that can be detected asymptotically in a minimax sense. We propose a simple testing procedure that has asymptotic optimal minimax properties for regular alternatives. We then adapt this procedure to testing the specification of a nonlinear parametric regression model. As a by-product, we obtain the rate of the optimal smoothing parameter that ensures optimal minimax properties for the test. We show that, by contrast, non-smoothing tests, such as Bierens' (1982) integrated conditional moment test, have undesirable minimax properties.
|Date of creation:||01 Aug 2000|
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- Joel Horowitz, 2000. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Econometric Society World Congress 2000 Contributed Papers 0166, Econometric Society.
- Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.