Open Access
August 2016 On high-dimensional sign tests
Davy Paindaveine, Thomas Verdebout
Bernoulli 22(3): 1745-1769 (August 2016). DOI: 10.3150/15-BEJ710


Sign tests are among the most successful procedures in multivariate nonparametric statistics. In this paper, we consider several testing problems in multivariate analysis, directional statistics and multivariate time series analysis, and we show that, under appropriate symmetry assumptions, the fixed-$p$ multivariate sign tests remain valid in the high-dimensional case. Remarkably, our asymptotic results are universal, in the sense that, unlike in most previous works in high-dimensional statistics, $p$ may go to infinity in an arbitrary way as $n$ does. We conduct simulations that (i) confirm our asymptotic results, (ii) reveal that, even for relatively large $p$, chi-square critical values are to be favoured over the (asymptotically equivalent) Gaussian ones and (iii) show that, for testing i.i.d.-ness against serial dependence in the high-dimensional case, Portmanteau sign tests outperform their competitors in terms of validity-robustness.


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Davy Paindaveine. Thomas Verdebout. "On high-dimensional sign tests." Bernoulli 22 (3) 1745 - 1769, August 2016.


Received: 1 June 2014; Revised: 1 October 2014; Published: August 2016
First available in Project Euclid: 16 March 2016

zbMATH: 1360.62225
MathSciNet: MR3474832
Digital Object Identifier: 10.3150/15-BEJ710

Keywords: high-dimensional tests , Portmanteau tests , sign tests , universal asymptotics

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 3 • August 2016
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