Statistical Science

Equitability, Interval Estimation, and Statistical Power

Yakir A. Reshef, David N. Reshef, Pardis C. Sabeti, and Michael Mitzenmacher

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Abstract

Emerging high-dimensional data sets often contain many nontrivial relationships, and, at modern sample sizes, screening these using an independence test can sometimes yield too many relationships to be a useful exploratory approach. We propose a framework to address this limitation centered around a property of measures of dependence called equitability. Given some measure of relationship strength, an equitable measure of dependence is one that assigns similar scores to equally strong relationships of different types. We formalize equitability within a semiparametric inferential framework in terms of interval estimates of relationship strength, and we then use the correspondence of these interval estimates to hypothesis tests to show that equitability is equivalent under moderate assumptions to requiring that a measure of dependence yield well-powered tests not only for distinguishing nontrivial relationships from trivial ones but also for distinguishing stronger relationships from weaker ones. We then show that equitability, to the extent it is achieved, implies that a statistic will be well powered to detect all relationships of a certain minimal strength, across different relationship types in a family. Thus, equitability is a strengthening of power against independence that enables exploration of data sets with a small number of strong, interesting relationships and a large number of weaker, less interesting ones.

Article information

Source
Statist. Sci., Volume 35, Number 2 (2020), 202-217.

Dates
First available in Project Euclid: 3 June 2020

Permanent link to this document
https://projecteuclid.org/euclid.ss/1591171227

Digital Object Identifier
doi:10.1214/19-STS719

Mathematical Reviews number (MathSciNet)
MR4106601

Keywords
Equitability measure of dependence statistical power independence test semiparametric inference

Citation

Reshef, Yakir A.; Reshef, David N.; Sabeti, Pardis C.; Mitzenmacher, Michael. Equitability, Interval Estimation, and Statistical Power. Statist. Sci. 35 (2020), no. 2, 202--217. doi:10.1214/19-STS719. https://projecteuclid.org/euclid.ss/1591171227


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