UNIVERSITY
OF ILLINOIS
DEPARTMENT OF STATISTICS
SEMINAR
NOTICE
The Department of Statistics
presents
Zhengjun Zhang
Washington University at St. Louis
"Quotient Correlation: A Sample Based Alternative to Pearson's Correlation"
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-squared, 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 correlation coefficient in
extreme value theory, and there does not exist an efficient tail
independence test statistic, these two new concepts may open up brand
new field of study. In addition, an
alternative to Spearman's rank correlation: rank based quotient
correlation is also defined. The advantages of using these new concepts
are illustrated in simulation data, and a real data analysis of air
pollutants as well.
These new measures and tests can be applied to many research and
practical areas, especially where the existing measures are not very
suitable. If time allows, I will show statistical evidences of the
existence of extreme co-movements and extreme impacts in the stock
market. Some findings are not consistent with the hypothesis, theory
used in the past in the financial world.
THURSDAY, September 2nd , 2004
4:00
P.M.
Room 2 Illini
Hall
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