Authors: Amro, Lubna
Title: Resampling-based inference methods for repeated measures data with missing values
Language (ISO): en
Abstract: The primary objective of this dissertation was to (i) develop novel resampling approaches for handling repeated measures data with missing values, (ii) compare their empirical power against other existing approaches using a Monte Carlo simulation study, and (iii) pinpoint the limitations of some common approaches, particularly for small sample sizes. This dissertation investigates four different statistical problems. The first is semiparametric inference for comparing means of matched pairs with missing data in both arms. Therein, we propose two novel randomization techniques; a weighted combination test and a multiplication combination test. They are based upon combining separate results of the permutation versions of the paired t-test and Welch test for the completely observed pairs and the incompletely observed components, respectively. As second problem, we consider the same setting but missingness in one arm only. There, we investigate a Wald-type statistic (WTS), an ANOVA-type statistic (ATS), and a modified ANOVA-type statistic (MATS). However, ATS and MATS are not distribution free under the null hypothesis, and WTS suffers from the slow convergence to its limiting 2 distribution. Thus, we develop asymptotic model-based bootstrap versions of these tests. The third problem is on nonparametric rank-based inference for matched pairs with incompleteness in both arms. In this more general setup, the only requirement is that the marginal distributions are not one point distributions. Therein, we propose novel multiplication combination tests that can handle three different testing problems, including the nonparametric Behrens-Fisher problem (Hp 0 : {p = 1/2}). Finally, the fourth problem is nonparametric rank-based inference for incompletely observed factorial designs with repeated measures. Therein, we develop a wild bootstrap approach combined with quadratic form-type test statistics (WTS, ATS, and MATS). These rank-based methods can be applied to both continuous and ordinal or ordered categorical data and (some) allow for singular covariance matrices. In addition to theoretically proving the asymptotic correctness of all the proposed procedures, extensive simulation studies demonstrate their favorable small samples properties in comparison to classical parametric tests. We also motivate and validate our approaches using real-life data examples from a variety of fields.
Subject Headings (RSWK): Teststatistik
Fehlende Daten
Inferenz <Statistik>
Randomisierter Test
Issue Date: 2022
Appears in Collections:Institut für Mathematische Statistik und industrielle Anwendungen

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