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Specification testing for transformation models with an application to generalized accelerated failure-time models. (English) Zbl 1331.62247
Summary: This paper provides a nonparametric test of the specification of a transformation model. Specifically, we test whether an observable outcome $$Y$$ is monotonic in the sum of a function of observable covariates $$X$$ plus an unobservable error $$U$$. Transformation models of this form are commonly assumed in economics, including, e.g., standard specifications of duration models and hedonic pricing models. Our test statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives violating the implied restriction. Monte Carlo experiments show that our test performs well in finite samples. We apply our results to test for specifications of generalized accelerated failure-time (GAFT) models of the duration of strikes.

##### MSC:
 62G10 Nonparametric hypothesis testing 62N05 Reliability and life testing 62P20 Applications of statistics to economics
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