Tests for heteroskedasticity in transformation models

Marie Hušková, Simos G. Meintanis () and Charl Pretorius
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Marie Hušková: Charles University
Simos G. Meintanis: National and Kapodistrian University of Athens
Charl Pretorius: North-West University

Statistical Papers, 2022, vol. 63, issue 4, No 2, 1013-1049

Abstract: Abstract We consider a model whereby a given response variable Y following a transformation $${{\mathcal {Y}}}:=\mathcal {T}(Y)$$ Y : = T ( Y ) , satisfies some classical regression equation. In this transformation model the form of the transformation is specified analytically but incorporates an unknown transformation parameter. We develop testing procedures for the null hypothesis of homoskedasticity for versions of this model where the regression function is considered either known or unknown. The test statistics are formulated on the basis of Fourier-type conditional contrasts of a variance computed under the null hypothesis against the same quantity computed under alternatives. The limit null distribution of the test statistic is studied, as well as the behaviour of the test criterion under alternatives. Since the limit null distribution is complicated, a bootstrap version is suggested in order to actually carry out the test procedures. Monte Carlo results are included that illustrate the finite-sample properties of the new method. The applicability of the new tests on real data is also illustrated.

Keywords: Transformation model; Heteroskedasticity test; Nonparametric regression; Bootstrap test (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-021-01267-8

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