Randomization Tests Under an Approximate Symmetry Assumption

Ivan A. Canay, Joseph P. Romano, Azeem M. Shaikh

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

This paper develops a theory of randomization tests under an approximate symmetry assumption. Randomization tests provide a general means of constructing tests that control size in finite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis. Here, by exhibits symmetry we mean that the distribution remains invariant under a group of transformations. In this paper, we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis. An important application of this idea is in settings where the data may be grouped into a fixed number of “clusters” with a large number of observations within each cluster. In such settings, we show that the distribution of the observed data satisfies our approximate symmetry requirement under weak assumptions. In particular, our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster, but also across clusters. This approach enjoys several advantages over other approaches in these settings.

Original languageEnglish (US)
Pages (from-to)1013-1030
Number of pages18
JournalEconometrica
Volume85
Issue number3
DOIs
StatePublished - May 2017

Keywords

  • Randomization tests
  • clustered data
  • dependence
  • differences-in-differences
  • heterogeneity
  • sign changes
  • symmetric distribution
  • weak convergence

ASJC Scopus subject areas

  • Economics and Econometrics

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