Next Article in Journal
Structures in Sound: Analysis of Classical Music Using the Information Length
Next Article in Special Issue
The Structure of the Class of Maximum Tsallis–Havrda–Chavát Entropy Copulas
Previous Article in Journal
Ensemble Equivalence for Distinguishable Particles
Previous Article in Special Issue
A Simulation-Based Study on Bayesian Estimators for the Skew Brownian Motion
Article Menu

Export Article

Open AccessArticle
Entropy 2016, 18(7), 256; doi:10.3390/e18070256

The Logical Consistency of Simultaneous Agnostic Hypothesis Tests

1
Institute of Mathematics and Statistics, University of São Paulo, São Paulo 13565-905, Brazil
2
Department of Statistics, Federal University of São Carlos, São Carlos 05508-090, Brazil
*
Author to whom correspondence should be addressed.
Academic Editor: Antonio M. Scarfone
Received: 30 May 2016 / Revised: 6 July 2016 / Accepted: 7 July 2016 / Published: 13 July 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
View Full-Text   |   Download PDF [365 KB, uploaded 13 July 2016]   |  

Abstract

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided. View Full-Text
Keywords: agnostic tests; multiple hypothesis testing; logical consistency; decision theory; loss functions agnostic tests; multiple hypothesis testing; logical consistency; decision theory; loss functions
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Esteves, L.G.; Izbicki, R.; Stern, J.M.; Stern, R.B. The Logical Consistency of Simultaneous Agnostic Hypothesis Tests. Entropy 2016, 18, 256.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top