Quotient correlation: A sample based alternative to Pearson’s correlation

By Zhengjun Zhang. 2008

65 citations recorded by the source corpus.

The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation coefficient is generally not applicable. One of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases where the Fisher's Z-transformation test may fail to reach a right conclusion. Unlike most asymptotic test statistics, which are either normal or Χ 2 , this test statistic has a limiting gamma distribution (henceforth, the gamma test statistic). More than the common usages of correlation, the quotient correlation can easily and intuitively be adjusted to values at tails. This adjustment generates two new concepts-the tail quotient correlation and the tail independence test statistics, which are also gamma statistics. Due to the fact that there is no analogue of the correlation coefficient in extreme value theory, and there does not exist an efficient tail independence test statistic, these two new concepts may open up a new field of study. In addition, an alternative to Spearman's rank correlation, a rank based quotient correlation, is also defined. The advantages of using these new concepts are illustrated with simulated data and a real data analysis of internet traffic.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/baf9b0ef13be2fed4fd436843bc99ed5d1a3a2a5

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Citations in the corpus

Upper tail dependence in rainfall extremes: would we know it if we saw it? (2015, methodology): “Following one of the recommendations of Frahm et al. (2005), we consider some formal statistical tests introduced by Falk and Michel (2006) and Zhang (2008).”
Testing Conditional Independence via Rosenblatt Transforms (2009, background): “See a recent paper by Zhang (2008) and references therein.”
Can cryptocurrencies be a safe haven: a tail risk perspective analysis (2018, methodology): “Alternatively, there are many other tail correlation estimation methods in the literature, for example, the tail quotient correlation coefficient (TQCC) method proposed by Zhang (2008), and Zhang, Zhang, and Cui (2017).”
Generalized Measures of Correlation for Asymmetry, Nonlinearity, and Beyond (2012, methodology): “Zhengjun Zhang is at the Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: zjz@stat.wisc.edu). The authors thank an editor, an associate editor, and two referees for their valuable comments and constructive suggestions that greatly improved the presentation of the article”