Comments on: An updated review of Goodness-of-Fit tests for regression models

We discuss the following two particular aspects of the paper of González-Manteiga and Crujeiras (<ExternalRef> <RefSource>10.1007/s11749-013-0327-5</RefSource> <RefTarget Address="10.1007/s11749-013-0327-5" TargetType="DOI"/> </ExternalRef>): First, what changes if the null hypothesis is non- or semiparametric? For example, Rodriguez-Poo et al. (A practical test for misspecification in regression: functional form, separability, and distribution. Econom. Theory, <CitationRef CitationID="CR28">2013</CitationRef>, 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? Sperlich (On the choice of regularization parameters in specification testing: a critical discussion. Empir. Econ., <CitationRef CitationID="CR29">2013</CitationRef>, forthcoming) 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 Dette (Ann. Stat. 27:1012–1040, <CitationRef CitationID="CR9">1999</CitationRef>) for nonparametric goodness-of-fit tests. Copyright Sociedad de Estadística e Investigación Operativa 2013