Academic Positions

  • Present 2023

    Teaching assistant

    University of Belgrade, Faculty of Organizational Sciences

  • 2023 2022

    Supporting assistant

    University of Belgrade, Faculty of Organizational Sciences

  • 2022 2021

    Supporting assistant

    University of Belgrade, Faculty of Mathematics

Education

  • PhD Studies of Mathematics Present

    University of Belgrade, Faculty of Mathematics

  • Master of Mathematics 2022

    University of Belgrade, Faculty of Mathematics

  • Bachelor of Mathematics 2021

    University of Belgrade, Faculty of Mathematics

  • High School 2017

    Grammar School "Vuk Karadžić", City of Loznica, Republic of Serbia

  • Elementary school 2013

    "Vuk Karadžić", Roćević, City of Zvornik, Republic of Srpska, Bosnia and Herzegovina

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A Novel Test of Missing Completely at Random: U-statistics-based Approach

Danijel Aleksić
arXiv preprint

Abstract

In this paper, a novel test for testing whether data are Missing Completely at Random is proposed. Asymptotic properties of the test are derived utilizing the theory of non-degenerate U-statistics. It is shown that the novel test statistic coincides with the well-known Little's statistic in the case of a univariate nonresponse. Then, the extensive simulation study is conducted to examine the performance of the test in terms of the preservation of type I error and in terms of power, under various underlying distributions, dimensions of the data and sample sizes. Performance of the Little's MCAR test is used as a benchmark for the comparison. The novel test shows better performance in all of the studied scenarios, better preserving the type I error and having higher empirical powers.

Non-degenerate U-statistics for data missing completely at random with application to testing independence

Danijel Aleksić, Marija Cuparić, Bojana Milošević
Stat

Abstract

Although the era of digitalization has enabled access to large quantities of data, due to their insufficient structuring, some data are often missing, and sometimes the percentage of missing data is significant compared to the entire sample. On the other hand, most of the statistical methodology is designed for complete data. Here we explore the asymptotic properties of non-degenerate U-statistics when the data are missing completely at random and a complete-case approach is utilized. The obtained results are applied to the estimator of Kendall's $tau$ used for testing independence. In this context, the median-based imputation approach is also considered and asymptotic properties are explored. In addition, both complete-case and median imputation approaches are compared in an extensive Monte Carlo study.

Abstract

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