A novel test of missing completely at random: U-statistics-based approach

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 $d^2$ statistic in the case of a multivariate data that has only one variable susceptible to missingness. 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. Various underlying distributions, dimensions of the data, sample sizes and alternatives are used. 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 for every studied alternative.

Keywords:

• Missing data
• missing completely at random
• novel test
• covariance
• asymptotic distribution
• power

2020 Mathematics Subject Classifications:

• 62G10
• 62G20
• 62H20

Acknowledgments

The author would like to thank the two anonymous referees whose comments have substantially improved the quality of this paper. The author would also like to thank professor Bojana Milošević from the University of Belgrade, Faculty of Mathematics, for fruitful discussions throughout creation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The work of D. Aleksić is supported by the Ministry of Science, Technological Development and Innovations of the Republic of Serbia (the contract 451-03-66/2024-03/200151).