Multiplication-combination tests for incomplete paired data

We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure. Dividing the observed data into dependent (completely observed) pairs and independent (incompletely observed) components, it is based on combining separate results of adequate tests for the two sub data sets. Our methods can be applied for parametric as well as semiparametric and nonparametric models and make use of all available data. In particular, the approaches are flexible and can be used to test different hypotheses in various models of interest. This is exemplified by a detailed study of mean- as well as rank-based approaches under different missingness mechanisms with different amount of missing data. Extensive simulations show that in most considered situations, the proposed procedures are more accurate than existing competitors particularly for the nonparametric Behrens-Fisher problem. A real data set illustrates the application of the methods.