A Simple Parametric Model Selection Test

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractWe propose a simple model selection test for choosing among two parametric likelihoods which can be applied in the most general setting without any assumptions on the relation between the candidate models and the true distribution. That is, both, one or neither is allowed to be correctly specified or misspecified, they may be nested, non-nested, strictly non-nested or overlapping. Unlike in previous testing approaches, no pre-testing is needed, since in each case, the same test statistic together with a standard normal critical value can be used. The new procedure controls asymptotic size uniformly over a large class of data generating processes. We demonstrate its finite sample properties in a Monte Carlo experiment and its practical relevance in an empirical application comparing Keynesian versus new classical macroeconomic models.

Model-selection tests for conditional moment restriction models

“…The use of extra randomness works in a fashion similar to the sample‐splitting techniques used in Yatchew () and Schennach and Wilhelm (), but instead of implicitly adding noise to the test statistic by sample‐splitting, we add the noise explicitly. One advantage of our approach relative to Yatchew is that the amount of noise added can be easily controlled and, in particular, can be made to vanish with sample size when it is not needed (i.e.…”

“…when ) . An advantage over the methods of both Yatchew () and Schennach and Wilhelm () is that our approach works for moment condition models when both models may have been correctly specified, while the sample‐splitting method does not correct the degeneracy in such cases. This is because for and , thereby causing even the sample‐splitting statistic to be degenerate.…”

“…As a result, our test simply uses the standard normal critical value and achieves asymptotic similarity. The adjustment simplifies the split‐sample idea of Yatchew () and Schennach and Wilhelm (), and achieves the same purpose as the latter. The difference in, and advantage of, our method over their method are discussed after the introduction of our test statistic in Section .…”

Pairwise model discrimination with applications in lifetime distributions and degradation processes

“…Consider two distribution families with respective densities f 1 ( x ; θ ) and f 2 ( x ; ξ ), where θ ∈ Θ and ξ ∈ Ξ are the model parameters, and Θ and Ξ are the corresponding parameter spaces. It is common to formulate the discrimination problem as the following hypothesis test (Schennach & Wilhelm, ) Based on the observed lifetime data D = { X 1 , …, X n }, the RML is then defined as where and are the ML estimators of θ and ξ based on D , respectively. ML estimators of commonly used distributions, including the log‐location‐scale distribution family, and the gamma and IG distributions, can be found in Meeker and Escobar ().…”

“…Some popular lifetime distributions include distributions in the log‐location‐scale family (eg, Weibull and log‐normal), the gamma distribution and the inverse Gaussian (IG) distribution (Chen, Ye, & Zhai, in press). A bulk of the literature have developed model discrimination techniques among these distributions, and a pairwise model discrimination procedure is often carried out (Schennach & Wilhelm, ; Vuong, ). In most of the existing studies, discrimination between two distributions is treated as a hypothesis test problem, and the test statistic is constructed as the logarithm of the ratio of maximized likelihoods (RML).…”