ENBIS-8 in Athens

21 – 25 September 2008 Abstract submission: 14 March – 11 August 2008

Cumulative copula charts for controlling the dependence among multivariate observations

22 September 2008, 15:20 – 15:40

Abstract

Submitted by
András Zempléni
Authors
András Zempléni, Pál Rakonczai, Csilla Hajas
Affiliation
Eötvös Loránd University, Budapest
Abstract
Dependence plays an important role in the properties of multivariate observation. In order to monitor possible changes in this aspect, beyond the usual approach of covariance estimation, we propose an additional control chart, which is sensitive to departures from the assumed dependence structure. This chart is cumulative in the sense that at every step all the available data to that time point is utilized.
We use the popular copula-approach for this approach. The copula allows for investigation the dependence structure separately from the univariate distributions, which is especially useful if the marginal distributions may change without causing an error, like in our case. Assuming that the standard charts deal with the univariate modeling as well as the changes in the mean vector, with the proposed new chart all aspects of important, possible changes are taken care for.
The fit of the observed copula to the one, considered as nullhypothesis can be measured by the multivariate version of the probability integral transform. Critical values can be constructed by simulation (see Rakonczai and A. Zempléni, 2007 for example). We illustrate the use of the chart by simulation studies and by real life bivariate data from our university, where the dependence between high-school final examination results and average achievements at the university is investigated.

Reference

P. Rakonczai and A. Zempléni, 2007: „ Copulas and goodness of fit tests " in: Recent Advances in Stochastic Modelling and Data Analysis, World Scientific, (Editor: C. Skiadas)
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