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Activity Number:
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136
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Type:
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Topic Contributed
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Date/Time:
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Monday, July 30, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #308251 |
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Title:
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Quotient Correlation: A Sample-Based Alternative to Pearson's Correlation
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Author(s):
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Zhengjun Zhang*+
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Companies:
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University of Wisconsin-Madison
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Address:
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Department of Statistics, Madison, WI, 53706,
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Keywords:
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necessary condition of tail independence ; nonparametric statistical coefficient ; semiparametric statistical coefficient ; dependence measure ; gamma distribution ; extreme value distribution
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Abstract:
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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 $\chi^2$, 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.
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