Mathematics – Statistics Theory
Scientific paper
2008-04-07
Annals of Statistics 2008, Vol. 36, No. 2, 1007-1030
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/009053607000000866 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053607000000866
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, 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.
No associations
LandOfFree
Quotient correlation: A sample based alternative to Pearson's correlation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quotient correlation: A sample based alternative to Pearson's correlation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quotient correlation: A sample based alternative to Pearson's correlation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-729883