COMPARING NONPARAMETRIC VERSUS PARAMETRIC REGRESSION FITS

In general, there will be visible differences between a parametric and a nonparametric curve estimate. It is therefore quite natural to comp are these in order to decide whether the parametric model could be jus tified. An asymptotic quantification is the distribution of the integr ated squared difference between these curves. We show that the standar d way of boot-strapping this statistic fails. We use and analyse a dif ferent form of bootstrapping for this task. We call this method the wi ld bootstrap and apply it to fitting Engel curves in expenditure data analysis.