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Metrika : Volume 80

Metrika : Volume 79

Metrika : Volume 66, Issue 3, November 2007

On model selection in Bayesian regression

On the inclusion of bivariate marked point processes in graphical models

Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

Games of chance with multiple objectives

Characterizations of negative multinomial distributions based on conditional distributions

Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence

Calibration methods for estimating quantiles

On the monitoring of multi-attributes high-quality production processes

Metrika : Volume 66, Issue 2, September 2007

Metrika : Volume 66, Issue 1, July 2007

Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence

Content Provider	Springer Nature Link
Author	Schmid, Friedrich Schmidt, Rafael
Copyright Year	2006
Abstract	We consider nonparametric estimation of multivariate versions of Blomqvist’s beta, also known as the medial correlation coefficient. For a two-dimensional population, the sample version of Blomqvist’s beta describes the proportion of data which fall into the first or third quadrant of a two-way contingency table with cutting points being the sample medians. Asymptotic normality and strong consistency of the estimators are established by means of the empirical copula process, imposing weak conditions on the copula. Though the asymptotic variance takes a complicated form, we are able to derive explicit formulas for large families of copulas. For the copulas of elliptically contoured distributions we obtain a variance stabilizing transformation which is similar to Fisher’s z-transformation. This allows for an explicit construction of asymptotic confidence bands used for hypothesis testing and eases the analysis of asymptotic efficiency. The computational complexity of estimating Blomqvist’s beta corresponds to the sample size n, which is lower than the complexity of most competing dependence measures.
Ending Page	354
Page Count	32
Starting Page	323
File Format	PDF
ISSN	00261335
e-ISSN	1435926X
Journal	Metrika
Issue Number	3
Volume Number	66
Language	English
Publisher	Springer-Verlag
Publisher Date	2006-12-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Order statistics; empirical distribution functions Copula Asymptotic properties Probability Theory and Stochastic Processes Asymptotic efficiency Statistics Distribution of statistics Blomqvist’s beta Asymptotic normality Statistics for Business/Economics/Mathematical Finance/Insurance Measures of association (correlation, canonical correlation, etc.) Empirical copula Economic Theory Tail dependence
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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