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Is there a non parametric version for Hotelling's $T^2$ test? Namely, the one group test for location (not the two group).

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  • $\begingroup$ Do you mean the largest root of a noncentral Wishart matrix? Like the solution to $|\lambda \Omega - Z'Z|=0$? $\endgroup$
    – Hirek
    Commented Feb 18, 2015 at 10:18
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    $\begingroup$ @Hirek: I want a test for the location of a multivariate symmetric (exchangeable?) distribution without the Gaussianity assumption. $\endgroup$
    – JohnRos
    Commented Feb 18, 2015 at 14:29
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    $\begingroup$ OK so your null hypothesis is the mean I gather. This one's hard because it is constructed as two Gaussians sandwhiching a Wishart matrix. Some terms to look up in the Journal of Multivariate Analysis or elsewhere would be central limit theorem (effect), T2 test, non-parametric etc. I got this methodology.psu.edu/media/techreports/13-124.pdf and also researchgate.net/publication/… The first seems to have what you look for. Also search for non-parametric Bartlett decomp.. $\endgroup$
    – Hirek
    Commented Feb 18, 2015 at 15:21
  • $\begingroup$ PS @JohnRos if you find either of my comments helpful, or the links in my previous one for that matter, you can upvote them as well! cheers! $\endgroup$
    – Hirek
    Commented Feb 18, 2015 at 15:26

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All it took was finding the right keywords to google. After finding and reading a bunch of papers, I found [1] to be an excellent reference with several non-parametric versions of Hotelling's one-sample $T^2$ test.

[1] Oja, Hannu, and Ronald H. Randles. “Multivariate Nonparametric Tests.” Statistical Science 19, no. 4 (November 1, 2004): 598–605.

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