When

Start: 10/17/2013 - 4:00pm

End : 10/17/2013 - 5:00pm

End : 10/17/2013 - 5:00pm

Category

Statistics/OR/Math Finance Seminar

Speaker

Uwe Schmock, TU, Vienna

Abstract

We discuss the performance of different estimators of dependence

measures, concentrating on the linear correlation coefficient and the

rank-based measure Kendall's tau. As the estimator of Kendall's tau

is a U-statistic, it is asymptotically normal. We calculate the

asymptotic variance explicitly for the Farlie-Gumbel-Morgenstern

copula, the Clayton copula, the Ali-Mikhail-Haq copula and the

Marshall-Olkin copula. For the Clayton copula, the result is

expressed using a generalized hypergeometric function, which can be

reduced to a more elementary form for specific parameters values of

the copula.

For elliptical distributions there is a unique connection between the

linear correlation coefficient and Kendall's tau. This offers two

ways for estimation: using the standard estimator of the linear

correlation directly or estimating Kendall's tau and transforming it

into a linear correlation estimate. Since both estimators are

asymptotically normal under appropriate moment conditions, we use the

asymptotic variance to compare their performance. For the

uncorrelated t-distribution, using the fact that it is a variance

mixture of normal distributions, we show that the asymptotic variance

equals an integral involving the square of the arctangent and a

hypergeometric function. For all integer-valued degrees of freedom,

involved and tricky integrations lead to a surprisingly simple closed

form for the asymptotic variance. It turns out that especially for

small degrees of freedom the alternative estimation via Kendall's tau

performs much better than the standard estimator. (This is joint work

with Barbara Dengler.)

Where

Roberts South 105, CMC