A Test of Independence in Two-Way Contingency Tables Based on Maximal Correlation

Yenigün, C. Deniz; Székely, Gábor; Rizzo, Maria L.

doi:10.1080/03610921003764274

Cited by 11 publications

(6 citation statements)

References 17 publications

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“…Two more recent publications are Huang (2010), where the maximal correlation is used to test for conditional independence, and Yenigün, Székely and Rizzo (2011), where it is used to test for independence in contingency tables. The latter paper introduces a new example where S(X, Y ) can be explicitly computed.…”

Section: Maximal Correlationmentioning

confidence: 99%

Statistical Dependence: Beyond Pearson’s ρ

2022

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Pearson's ρ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known; however, that it has a number of shortcomings; in particular, for heavy tailed distributions and in nonlinear situations, where it may produce misleading, and even disastrous results. In recent years, a number of alternatives have been proposed. In this paper, we will survey these developments, especially results obtained in the last couple of decades. Among measures discussed are the copula, distribution-based measures, the distance covariance, the HSIC measure popular in machine learning and finally the local Gaussian correlation, which is a local version of Pearson's ρ. Throughout, we put the emphasis on conceptual developments and a comparison of these. We point out relevant references to technical details as well as comparative empirical and simulated experiments. There is a broad selection of references under each topic treated.

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Section: Maximal Correlationmentioning

confidence: 99%

Statistical Dependence: Beyond Pearson’s ρ

2022

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“…Two more recent publications are Huang (2010), where the maximal correlation is used to test for conditional independence, and Yenigün, Székely, and Rizzo (2011), where it is used to test for independence in contingency tables. The latter paper introduces a new example where S(X, Y ) can be explicitly computed.…”

Section: Maximal Correlationmentioning

confidence: 99%

Statistical dependence: Beyond Pearson's $ρ$

Tjøstheim,

Otneim,

Støve

2018

Preprint

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Pearson's ρ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a number of shortcomings; in particular for heavy tailed distributions and in nonlinear situations, where it may produce misleading, and even disastrous results. In recent years a number of alternatives have been proposed. In this paper, we will survey these developments, especially results obtained in the last couple of decades. Among measures discussed are the copula, distribution-based measures, the distance covariance, the HSIC measure popular in machine learning, and finally the local Gaussian correlation, which is a local version of Pearson's ρ. Throughout we put the emphasis on conceptual developments and a comparison of these. We point out relevant references to technical details as well as comparative empirical and simulated experiments. There is a broad selection of references under each topic treated.

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“…The new method consistently yields an estimated p-value approximate to the exact result. Yenigün et al (2011) carried out a simulation study to observe the empirical power performance of the maximal correlation test and compared it with 2 and 2 independence tests. When the underlying continuous variables are uncorrelated but dependent, the authors pointed out some cases for which the maximal correlation test appears to be more powerful.…”

Section: Introductionmentioning

confidence: 99%

The LMS for testing independence in two-way contingency tables

Sulewski

2019

Biometrical Letters

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SummaryIn the statistical literature there are proposed many test measures to determine the independence of two qualitative variables in contingency tables, in particular in two-way contingency tables larger than 2×2. For statistical analysis, three of the so-called “chi-squared tests”—the T3 test, BP test and |χ| test—were selected. These tests were compared with a logarithmic minimum test, which is the author’s proposal. Critical values for the tests were determined with the Monte Carlo method. To compare the tests, an appropriate measure of untruthfulness of H0 was used and the power of the tests was calculated.

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A Test of Independence in Two-Way Contingency Tables Based on Maximal Correlation

Cited by 11 publications

References 17 publications

Statistical Dependence: Beyond Pearson’s ρ

Statistical Dependence: Beyond Pearson’s ρ

Statistical dependence: Beyond Pearson's $ρ$

The LMS for testing independence in two-way contingency tables

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