Asymptotics of empirical copula processes under non-restrictive smoothness assumptions

DOI10.3150/11-BEJ387zbMath1243.62066arXiv1012.2133OpenAlexW2081534887MaRDI QIDQ442074

Johan Segers

Publication date: 9 August 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2133

zbMATH Keywords

weak convergenceempirical processesBrownian bridgetail dependencemultiplier central limit theoremArchimedean copulasempirical copulasextreme-value copulasGaussian copulas

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Order statistics; empirical distribution functions (62G30) Statistics of extreme values; tail inference (62G32) Strong limit theorems (60F15)

Related Items (only showing first 100 items - show all)

A random walk through Canadian contributions on empirical processes and their applications in probability and statistics ⋮ Testing symmetry for bivariate copulas using Bernstein polynomials ⋮ Wavelet block thresholding for copula density estimation under biased sampling ⋮ Estimation and inference in factor copula models with exogenous covariates ⋮ When copulas and smoothing met: an interview with Irène Gijbels ⋮ A novel positive dependence property and its impact on a popular class of concordance measures ⋮ Testing for independence in high dimensions based on empirical copulas ⋮ A class of smooth, possibly data-adaptive nonparametric copula estimators containing the empirical beta copula ⋮ Copula modeling from Abe Sklar to the present day ⋮ Estimation of Copulas via Maximum Mean Discrepancy ⋮ Unnamed Item ⋮ On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators ⋮ The Copula Information Criteria ⋮ Uncertainty quantification in complex simulation models using ensemble copula coupling ⋮ TESTING FOR CHANGES IN KENDALL’S TAU ⋮ RANDOMIZATION TESTS OF COPULA SYMMETRY ⋮ A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing ⋮ A general framework for testing homogeneity hypotheses about copulas ⋮ Detecting breaks in the dependence of multivariate extreme-value distributions ⋮ Nonparametric recursive estimation of the copula ⋮ The cross-quantilogram: measuring quantile dependence and testing directional predictability between time series ⋮ Estimation of risk measures in energy portfolios using modern copula techniques ⋮ A fluctuation test for constant Spearman's rho with nuisance-free limit distribution ⋮ Nonparametric estimation of pair-copula constructions with the empirical pair-copula ⋮ Non‐parametric Copula Estimation Under Bivariate Censoring ⋮ Estimation of a Copula when a Covariate Affects only Marginal Distributions ⋮ A simple non-parametric goodness-of-fit test for elliptical copulas ⋮ Choice of smoothing parameter in multivariate copula-based tail coefficients ⋮ Inference for asymptotically independent samples of extremes ⋮ Multiple block sizes and overlapping blocks for multivariate time series extremes ⋮ Nonparametric inference on Lévy measures and copulas ⋮ Nonparametric Identification of Copula Structures ⋮ Directional differentiability for supremum-type functionals: statistical applications ⋮ On the asymptotic covariance of the multivariate empirical copula process ⋮ Asymptotic behavior of weighted multivariate Cramér-von Mises-type statistics under contiguous alternatives ⋮ Empirical copulas for consecutive survival data ⋮ Tests of symmetry for bivariate copulas ⋮ Efficient semiparametric copula estimation of regression models with endogeneity ⋮ Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique ⋮ Empirical and sequential empirical copula processes under serial dependence ⋮ Measuring association and dependence between random vectors ⋮ A note on the asymptotic behavior of the Bernstein estimator of the copula density ⋮ On the empirical multilinear copula process for count data ⋮ A copula approach for dependence modeling in multivariate nonparametric time series ⋮ On the strong approximation of bootstrapped empirical copula processes with applications ⋮ Large sample properties of nonparametric copula estimators under bivariate censoring ⋮ A censored copula model for micro-level claim reserving ⋮ Rank correlation under categorical confounding ⋮ Partial and average copulas and association measures ⋮ Test of symmetry based on copula function ⋮ Inference for Archimax copulas ⋮ Estimating multivariate extremal dependence: a new proposal ⋮ Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines ⋮ Goodness-of-fit testing for copulas: a distribution-free approach ⋮ Multivariate and functional covariates and conditional copulas ⋮ Nonparametric Inference for Copulas and Measures of Dependence Under Length-Biased Sampling and Informative Censoring ⋮ Weighted estimation of the dependence function for an extreme-value distribution ⋮ The multivariate piecing-together approach revisited ⋮ Nonparametric estimation of multivariate extreme-value copulas ⋮ When uniform weak convergence fails: empirical processes for dependence functions and residuals via epi- and hypographs ⋮ GOODNESS-OF-FIT TESTS FOR MULTIVARIATE COPULA-BASED TIME SERIES MODELS ⋮ On tests of radial symmetry for bivariate copulas ⋮ On the specification of multivariate association measures and their behaviour with increasing dimension ⋮ Multivariate multiple test procedures based on nonparametric copula estimation ⋮ Nonparametric tests for tail monotonicity ⋮ General tests of independence based on empirical processes indexed by functions ⋮ Using B-splines for nonparametric inference on bivariate extreme-value copulas ⋮ Extreme value copula estimation based on block maxima of a multivariate stationary time series ⋮ Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case ⋮ Detecting departures from meta-ellipticity for multivariate stationary time series ⋮ Tail-weighted dependence measures with limit being the tail dependence coefficient ⋮ Mass distributions of two-dimensional extreme-value copulas and related results ⋮ Kac's representation for empirical copula process from an asymptotic viewpoint ⋮ The empirical beta copula ⋮ On the weak convergence of the empirical conditional copula under a simplifying assumption ⋮ Weak convergence of the weighted empirical beta copula process ⋮ Some applications of the strong approximation of the integrated empirical copula processes ⋮ Nonparametric estimation of multivariate tail probabilities and tail dependence coefficients ⋮ Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials ⋮ Rank-based inference tools for copula regression, with property and casualty insurance applications ⋮ Asymptotic behavior of the empirical multilinear copula process under broad conditions ⋮ Weak convergence of empirical and bootstrapped \(C\)-power processes and application to copula goodness-of-fit ⋮ Subsampling (weighted smooth) empirical copula processes ⋮ Weighted least-squares inference for multivariate copulas based on dependence coefficients ⋮ Detecting changes in cross-sectional dependence in multivariate time series ⋮ Copula-based dynamic models for multivariate time series ⋮ Tests of stochastic monotonicity with improved power ⋮ Asymptotic total variation tests for copulas ⋮ Some results on change-point detection in cross-sectional dependence of multivariate data with changes in marginal distributions ⋮ On metric spaces of subcopulas ⋮ Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions ⋮ Empirical tail copulas for functional data ⋮ Spatially homogeneous copulas ⋮ Non-parametric weighted tests for independence based on empirical copula process ⋮ Validation of association ⋮ Change-point problems for multivariate time series using pseudo-observations ⋮ On nonparametric tests of multivariate meta-ellipticity ⋮ A note on conditional versus joint unconditional weak convergence in bootstrap consistency results ⋮ Central limit theorem for subcopulas under the Manhattan distance ⋮ Non-parametric estimator of a multivariate madogram for missing-data and extreme value framework

Uses Software

• TwoCop

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on bootstrap approximations for the empirical copula process
• The oscillation behavior of empirical processes: The multivariate case
• Rank-based inference for bivariate extreme-value copulas
• Improved kernel estimation of copulas: weak convergence and goodness-of-fit testing
• Multivariate Archimedean copulas, \(d\)-monotone functions and \(\ell _{1}\)-norm symmetric distributions
• On the covariance of the asymptotic empirical copula process
• Nonparametric rank-based tests of bivariate extreme-value dependence
• Asymptotic local efficiency of Cramér\,-\,von Mises tests for multivariate independence
• Testing for equality between two copulas
• Tests of independence among continuous random vectors based on Cramér-von Mises functionals of the empirical copula process
• Extremal theory for stochastic processes
• Laws of the iterated logarithm in the tails for weighted uniform empirical processes
• Bounds for weighted empirical distribution functions
• Asymptotic distributions of multivariate rank order statistics
• Weak convergence of empirical copula processes
• Weak convergence and empirical processes. With applications to statistics
• Tests of independence and randomness based on the empirical copula process
• Empirical processes indexed by estimated functions
• Nonparametric estimation of copula functions for dependence modelling
• Semiparametric estimation in copula models
• A kolmogorov-smirnov type test for positive quadrant dependence

This page was built for publication: Asymptotics of empirical copula processes under non-restrictive smoothness assumptions