Smoothed Bootstrap und seine Anwendung in parametrischen Testverfahren

Abstract

In empirical research, the distribution of observations is usually unknown. This creates a problem if parametric methods are to be employed. The functionality of parametric methods relies on strong parametric assumptions. If these are violated the result of using classical parametric methods is questionable. Therefore, modifications of the parametric methods are required, if the appropriateness of their assumptions is in doubt. In this article, a modification of the smoothed bootstrap is presented (using the linear interpolation) to approximate the distribution law suggested by the data. The application of this modification to statistical parametric methods allows taking into account deviations of the observed data distributions from the classical distribution assumptions without changing to other hypotheses, which often is implicit in using nonparametric methods. The approach is based on Monte Carlo method and is presented using one-way ANOVA as an example. The original and the modified statistical methods lead to identical outcomes when the assumptions of the original method are satisfied. For strong violations of the distributional assumptions, the modified version of the method is generally preferable. All procedures have been implemented in SAS. Test characteristics (type 1 error, the operating characteristic curve) of the modified ANOVA are calculated.

Keywords

• distributional assumption
• resampling
• inverse transform sampling
• Monte Carlo method
• ANOVA