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Description

Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings, and to the best of our knowledge, there are no established goodness-of-fit tests for elliptical models that are supported by theoretical guarantees in high dimensions. In this work, we propose a new goodness-of-fit test for this problem, and our main result shows that the test is asymptotically valid when the dimension and sample size diverge proportionally. Remarkably, it also turns out that the asymptotic validity of the test requires no assumptions on the population covariance matrix. Lastly, we will discuss some more recent work extending these ideas to a goodness-of-fit test for independent component models in high dimensions. (A subset of this work will appear in JASA: https://doi.org/10.1080/01621459.2025.2518617. Joint work with Siyao Wang and Mingshuo Liu.)