Descriptor: "Multivariate measure of association" - Searchworks@Jio Institute Digital Library Search Results

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Author: Gaißer, Sandra, Ruppert, Martin, and Schmid, Friedrich
Subjects: *MULTIVARIATE analysis, *MEASURE theory, *COPULA functions, *SIMULATION methods & models, *ASYMPTOTIC expansions, *NONPARAMETRIC statistics, *ANALYSIS of variance, *ASSETS (Accounting), *STATISTICAL bootstrapping
Abstract: Abstract: A multivariate measure of association is proposed, which extends the bivariate copula-based measure Phi-Square introduced by Hoeffding . We discuss its analytical properties and calculate its explicit value for some copulas of simple form; a simulation procedure to approximate its value is provided otherwise. A nonparametric estimator for multivariate Phi-Square is derived and its asymptotic behavior is established based on the weak convergence of the empirical copula process both in the case of independent observations and dependent observations from strictly stationary strong mixing sequences. The asymptotic variance of the estimator can be estimated by means of nonparametric bootstrap methods. For illustration, the theoretical results are applied to financial asset return data. [ABSTRACT FROM AUTHOR]
Published: 2010
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Author: Schmid, Friedrich and Schmidt, Rafael
Subjects: *MULTIVARIATE analysis, *STATISTICS, *COPULA functions, *ESTIMATION theory
Abstract: Abstract: Multivariate measures of association are considered which, in the bivariate case, coincide with the population version of Spearman''s rho. For these measures, nonparametric estimators are introduced via the empirical copula. Their asymptotic normality is established under rather weak assumptions concerning the copula. The asymptotic variances are explicitly calculated for some copulas of simple structure. For general copulas, a nonparametric bootstrap is established. [Copyright &y& Elsevier]
Published: 2007
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Author: Sandra Gaiíer, Martin Ruppert, and Friedrich Schmid
Subjects: Statistics and Probability, Multivariate statistics, Numerical Analysis, Statistics::Theory, Weak convergence, Empirical copula process, Copula (linguistics), Estimator, Multivariate measure of association, Bivariate analysis, Stationary sequence, Nonparametric bootstrap, Delta method, Copula, Strong mixing, Econometrics, Applied mathematics, Statistics::Methodology, Statistics, Probability and Uncertainty, Nonparametric estimation, Hoeffding's inequality, Mathematics
Abstract: A multivariate measure of association is proposed, which extends the bivariate copula-based measure Phi-Square introduced by Hoeffding [22]. We discuss its analytical properties and calculate its explicit value for some copulas of simple form; a simulation procedure to approximate its value is provided otherwise. A nonparametric estimator for multivariate Phi-Square is derived and its asymptotic behavior is established based on the weak convergence of the empirical copula process both in the case of independent observations and dependent observations from strictly stationary strong mixing sequences. The asymptotic variance of the estimator can be estimated by means of nonparametric bootstrap methods. For illustration, the theoretical results are applied to financial asset return data.
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