Specification testing in semi-parametric transformation models

Nick Kloodt (), Natalie Neumeyer and Ingrid Keilegom
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Nick Kloodt: Universität Hamburg
Natalie Neumeyer: Universität Hamburg
Ingrid Keilegom: KU Leuven

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 4, No 8, 980-1003

Abstract: Abstract In transformation regression models, the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression function is modeled nonparametrically. We suggest a test for goodness-of-fit of a parametric transformation class based on a distance between a nonparametric transformation estimator and the parametric class. We present asymptotic theory under the null hypothesis of validity of the semi-parametric model and under local alternatives. A bootstrap algorithm is suggested in order to apply the test. We also consider relevant hypotheses to distinguish between large and small distances of the parametric transformation class to the ‘true’ transformation.

Keywords: Bootstrap; Goodness-of-fit test; Nonparametric regression; Nonparametric transformation estimator; Parametric transformation class; U-statistics; 62G10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11749-021-00756-0

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