Multiplication-Combination Tests for Incomplete Paired Data

TL;DR

This paper introduces a new multiplication combination testing procedure for incomplete paired data that enhances accuracy by effectively utilizing all available data across parametric and nonparametric models.

Contribution

It proposes a novel multiplication combination method that improves hypothesis testing accuracy for incomplete paired data, applicable to various models and hypotheses.

Findings

Proposed methods outperform existing tests in accuracy.

Flexible approach applicable to parametric, semi-, and nonparametric models.

Effective use of all available data in hypothesis testing.

Abstract

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 datasets. Our methods can be applied for parametric as well as semi- and nonparametric models and make efficient 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 apporaches. Extensive simulations show that the proposed procedures are more accurate than existing competitors. A real data set illustrates the application of the methods.