arXiv subjects
Publications and source records attributed to Danijel G. Aleksić.
We prove a novel characterization of the exponential distribution via a linear combination of order statistics. The theorem established herein generalizes the previous characterization theorem given in Milošević and Obradović (2016a). The proof relies on properties of Stirling numbers of the second kind, which are derived for this purpose and may be of independent interest.
This paper presents a generalized version of a U-statistics-based test for MCAR developed by Aleksić (2024). The proposed test, similar to the original, evaluates the MCAR assumption by calculating and combining the covariances between response indicators and data variables. However, unlike the preceding version, it is capable of utilizing partially observed variables, resulting in a significantly larger class of detectable alternatives. Numerical results indicate that the improved test is well-calibrated, notably outperforming the well-known MCAR test developed by Little (1988) used as a benchmark. For alternatives detectable by the original method, the improved test maintains comparable, although slightly lower, power, while consistently outperforming Little's test across all studied scenarios. For alternatives that were previously undetectable or marginally detectable, the novel test demonstrates the superior performance among the three methods. While the novel test shares the assumption of finite fourth moments of the data with Little's test, the results suggest it is more robust to this requirement, although both tests exhibit similar limitations.
In this paper, we address the problem of two-sample testing in the presence of missing data under a variety of missingness mechanisms. Our focus is on the well-known energy distance-based two-sample test. In addition to the standard complete-case approach, we propose a modification of the test statistic that incorporates all available data, utilizing appropriate weights. The asymptotic null distribution of the test statistic is derived and two resampling procedures for approximating the corresponding p-values are proposed. We also propose a new bootstrap method specifically designed for a test statistic based on samples completed via common imputation methods. Through an extensive simulation study, we compare all methods in terms of type I error control and statistical power across a set of sample sizes, dimensions, distributions, missingness mechanisms, and missingness rates. Based on these results, we provide general recommendations for each considered scenario.