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Title: Tests for heteroskedasticity in transformation models Authors:  Charl Pretorius - North-West University (South Africa) [presenting]
Simos Meintanis - University of Athens (Greece)
Marie Huskova - Charles University (Czech Republic)
Abstract: A model is considered whereby a given response variable $Y$ following a transformation $\mathcal{T}(Y)$ satisfies some classical regression equation. In this transformation model, the form of the transformation is specified analytically but incorporates an unknown transformation parameter that needs to be estimated. We develop testing procedures for the null hypothesis of homoskedasticity for versions of this model where the regression function is considered to be 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 and involves many unknown quantities, a bootstrap scheme is suggested in order to carry out the test procedures. Monte Carlo results, which illustrate the finite-sample properties of the new procedures, will also be presented.