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An Invariant Test for Equality of Two Large Scale Covariance Matrices

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Taehyeon Koo, Seonghun Cho, Johan Lim

Statistics Theory · Submitted 14 Nov 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We numerically show that our test has higher power than two modified likelihood ratio tests by Zhang et al. (2019) in all cases both we and they consider.

how it is stated · asserted 1.00 read the record →

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arXiv ID1911.06006 (version 1)
Pith IDVLDV3HXM, Pith's permanent record of this paper and its review
CitationJohan Lim, Seonghun Cho, Taehyeon Koo. "An Invariant Test for Equality of Two Large Scale Covariance Matrices." arXiv:1911.06006 (2019). https://pith.science/paper/VLDV3HXM
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,444 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.27 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this work, we are motivated by the recent work of Zhang et al. (2019) and study a new invariant test for equality of two large scale covariance matrices. Two modified likelihood ratio tests (LRTs) by Zhang et al. (2019) are based on the sum of log of eigenvalues (or 1- eigenvalues) of the Beta-matrix. However, as the dimension increases, many eigenvalues of the Beta-matrix are close to 0 or 1 and the modified LRTs are greatly influenced by them. In this work, instead, we consider the simple sum of the eigenvalues (of the Beta-matrix) and compute its asymptotic normality when all $n_1, n_2, p$ increase at the same rate. We numerically show that our test has higher power than two modified likelihood ratio tests by Zhang et al. (2019) in all cases both we and they consider.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this work, we are motivated by the recent work of Zhang et al. (2019) and study a new invariant test for equality of two large scale covariance matrices. contribution 0.84 0.43 0.06 asserted 0.90
s1 Two modified likelihood ratio tests (LRTs) by Zhang et al. (2019) are based on the sum of log of eigenvalues (or 1- eigenvalues) of the Beta-matrix. background 1.00 0.04 0.03 asserted 1.00
s2 However, as the dimension increases, many eigenvalues of the Beta-matrix are close to 0 or 1 and the modified LRTs are greatly influenced by them. gap 0.59 0.19 0.03 asserted 1.00
s3 In this work, instead, we consider the simple sum of the eigenvalues (of the Beta-matrix) and compute its asymptotic normality when all $n_1, n_2, p$ increase at the same rate. method 0.60 0.96 0.17 asserted 0.98
s4 We numerically show that our test has higher power than two modified likelihood ratio tests by Zhang et al. (2019) in all cases both we and they consider. result 1.00 0.95 0.74 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.98 · evidence from simulation or computation 0.87.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this work, we are motivated by the recent work of Zhang et al. (2019) and study a new invariant test for equality of two large scale covariance matrices. Two modified likelihood ratio tests (LRTs) by Zhang et al. (2019) are based on the sum of log of eigenvalues (or 1- eigenvalues) of the Beta-matrix. However, as the dimension increases, many eigenvalues of the Beta-matrix are close to 0 or 1 and the modified LRTs are greatly influenced by them. In this work, instead, we consider the simple sum of the eigenvalues (of the Beta-matrix) and compute its asymptotic normality when all $n_1, n_2, p$ increase at the same rate. We numerically show that our test has higher power than two modified likelihood ratio tests by Zhang et al. (2019) in all cases both we and they consider.

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