Two-sample tests for high-dimension, strongly spiked eigenvalue models

By Makoto Aoshima, Kazuyoshi Yata. 2016

57 citations recorded by the source corpus.

We consider two-sample tests for high-dimensional data under two disjoint models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. We provide a general test statistic as a function of a positive-semidefinite matrix. We give sufficient conditions for the test statistic to satisfy a consistency property and to be asymptotically normal. We discuss an optimality of the test statistic under the NSSE model. We also investigate the test statistic under the SSE model by considering strongly spiked eigenstructures and create a new effective test procedure for the SSE model. Finally, we discuss the performance of the classifiers numerically.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2c823dbfefcfb13b9dcd321c26a00a575bc527c0

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In Statistics and Probability

1. Ming-Yen Cheng
2. Bu Zhou
3. Jia Guo
4. Jin-Ting Zhang
5. Xuehua Liang
6. Jing Lei
7. Adela Martínez-Calvo
8. Yixin Fang

Citations in the corpus

• A Simple Two-Sample Test in High Dimensions Based on L2-Norm (2020, background): “…require any structural assumptions on the covariance matrix such as spiked eigenvalue models considered by Katayama, Kanoa, and Srivastava (2013), Aoshima and Yata (2018), and others, nor it assumes restrictive conditions on the covariance matrix such as (8)–(10) imposed by Bai and Saranadasa…”