Asymptotic-based bootstrap approach for matched pairs with missingness in a single arm

The issue of missing values is an arising difficulty when dealing with paired data. Several test procedures are developed in the literature to tackle this problem. Some of them are even robust under deviations and control type-I error quite accurately. However, most of these methods are not applicable when missing values are present only in a single arm. For this case, we provide asymptotic correct resampling tests that are robust under heteroskedasticity and skewed distributions. The tests are based on a meaningful restructuring of all observed information in quadratic form–type test statistics. An extensive simulation study is conducted exemplifying the tests for finite sample sizes under different missingness mechanisms. In addition, illustrative data examples based on real life studies are analyzed

Testing Equality Of Two Normal Means Using Combined Samples Of Paired And Unpaired Data

A test for equality of two normal means when the data consist of both paired and unpaired observations is proposed. The proposed test is compared with two other standard methods known in the literature with respect to the type I error rate and power using simulation results

Resampling-based inference methods for repeated measures data with missing values

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

Statistical inference with paired observations and independent observations in two samples

A frequently asked question in quantitative research is how to compare two samples that include some combination of paired observations and unpaired observations. This scenario is referred to as `partially overlapping samples'. Most frequently the desired comparison is that of central location. Depending on the context, the research question could be a comparison of means, distributions, proportions or variances. Approaches that discard either the paired observations or the independent observations are customary. Existing approaches evoke much criticism. Approaches that make use of all available data are becoming more prominent. Traditional and modern approaches for the analyses for each of these research questions are reviewed. Novel solutions for each of the research questions are developed and explored using simulation. Results show that proposed tests which report a direct measurable difference between two groups provide the best solutions