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Comments on: “An updated review of goodness-of-fit tests for regression models”. (English) Zbl 1367.62126
Summary: We discuss the following two particular aspects of the paper of W. González-Manteiga and R. M. Crujeiras [Test 22, No. 3, 361–411 (2013; Zbl 1273.62086)]: First, what changes if the null hypothesis is non- or semiparametric? For example, J. Rodriguez-Poo et al. [“A practical test for misspecification in regression: functional form, separability, and distribution”, Econ. Theor. (under revision)] considered optimal rates of adaptive nonparametric tests when the null model is semiparametric. A second, though related question is, how serious are the bandwidth and calibration problems? In [“On the choice of regularization parameters in specification testing: a critical discussion”, Empir. Econ. 47, No. 2, 427–450 (2013; doi:10.1007/s00181-013-0752-z)], the author has shown that the unsolved bandwidth selection problems, in particular when calibrating, render nonparametric specification tests useless in practice. Two additional questions are only raised briefly and concern (a) the computational aspects, and (b) the problem that asymptotically, nonparametric omnibus tests might reject almost any null hypothesis as probably no parametric or semiparametric model is 100% correct. But it is maybe a reasonable and useful approximation. To this aim we recall the idea of testing the problem of so-called ‘precise hypotheses’ as outlined in [H. Dette, Ann. Stat. 27, No. 3, 1012–1040 (1999; Zbl 0957.62036)] for nonparametric goodness-of-fit tests.

62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
62-02 Research exposition (monographs, survey articles) pertaining to statistics
Full Text: DOI
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