A Comparison of Two Bootstrap Schemes on Goodness of Fit Tests in Presence of Selection Bias

If a data set suffers from selection bias then, ordinary regression estimators must be adapted in order to achieve consistency. Consequently, it is necessary to modify any goodness of fit tests based on distances between parametric and non-parametric residuals. More particularly, any bootstrap approximation to these tests must be re– designed. Our first approach to this latter task is based on a resampling of nonparametric residuals in order to obtain dependent variable bootstrap values and plug them into the adapted estimators. The second approach consists of a resampling of weighted residuals, which compensates the selection bias in a such way that ordinary regression estimators could be used. Both alternatives are theoretically analyzed and some simulations studies are carried out to illustrate the behaviour of the two approaches with finite samples.