• Bernoulli
  • Volume 22, Number 3 (2016), 1745-1769.

On high-dimensional sign tests

Davy Paindaveine and Thomas Verdebout

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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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Bernoulli, Volume 22, Number 3 (2016), 1745-1769.

Received: June 2014
Revised: October 2014
First available in Project Euclid: 16 March 2016

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high-dimensional tests Portmanteau tests sign tests universal asymptotics


Paindaveine, Davy; Verdebout, Thomas. On high-dimensional sign tests. Bernoulli 22 (2016), no. 3, 1745--1769. doi:10.3150/15-BEJ710.

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Supplemental materials

  • Supplement to “High-dimensional sign tests”. The supplement article contains the proofs of Theorems 2.4 and 2.5 together with simulation results related to the sign test for independence. It also provides histograms from the simulations of Section 3.1.