Testing the adequacy of semiparametric transformation models

J. S. Allison (), M. Hušková () and S. G. Meintanis ()
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J. S. Allison: North-West University
M. Hušková: Charles University
S. G. Meintanis: North-West University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 1, No 5, 70-94

Abstract: Abstract We consider a semiparametric model whereby the response variable following a transformation can be expressed by means of a regression model. In this model, the form of the transformation is specified analytically (up to an unknown transformation parameter), while the regression function is completely unknown. We develop testing procedures for the null hypothesis that this semiparametric model adequately describes the data at hand. In doing so, the test statistic is formulated on the basis of Fourier-type conditional expectations, an idea first put forward by Bierens (J Econom 20:105–134, 1982). The asymptotic distribution of the test statistic is obtained under the null as well as under alternative hypotheses. Since the limit null distribution is nonstandard, a bootstrap version is utilized in order to actually carry out the test procedure. Monte Carlo results are included that illustrate the finite-sample properties of the new method.

Keywords: Transformation model; Goodness-of-fit test; Nonparametric regression; Bootstrap test; 62G08; 62G09; 62G10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11749-017-0544-4

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