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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning 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A Novel Test of Missing Completely at Random: U-statistics-based Approach
Danijel Aleksić · 2023-10-30 · via math.ST updates on arXiv.org

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.

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