Goodness-of-fit tests in semiparametric transformation models
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Benjamin Colling [1] ; Ingrid Van Keilegom [1]
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[1] Université Catholique de Louvain
Université Catholique de Louvain
Arrondissement de Nivelles, Bélgica
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 25, Nº. 2, 2016, págs. 291-308
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
Consider a semiparametric transformation model of the form Λθ(Y) =m(X)+ε, where Y is a univariate dependent variable, X is a d-dimensional covariate, and ε is independent of X and has mean zero. We assume that {Λθ:θ∈Θ} is a parametric family of strictly increasing functions, while m is an unknown regression function. The goal of the paper is to develop tests for the null hypothesis that m(⋅) belongs to a certain parametric family of regression functions. We propose a Kolmogorov–Smirnov and a Cramér–von Mises type test statistic, which measure the distance between the distribution of ε estimated under the null hypothesis and the distribution of ε without making use of this null hypothesis. The estimated distributions are based on a profile likelihood estimator of θ and a local polynomial estimator of m(⋅). The limiting distributions of these two test statistics are established under the null hypothesis and under a local alternative. We use a bootstrap procedure to approximate the critical values of the test statistics under the null hypothesis. Finally, a simulation study is carried out to illustrate the performance of our testing procedures, and we apply our tests to data on the scattering of sunlight in the atmosphere.
