Related papers: Weak convergence of the weighted empirical beta co…
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…
Weak convergence of the empirical copula process indexed by a class of functions is established. Two scenarios are considered in which either some smoothness of these functions or smoothness of the underlying copula function is required. A…
The empirical beta copula is a simple but effective smoother of the empirical copula. Because it is a genuine copula, from which, moreover, it is particularly easy to sample, it is reasonable to expect that resampling procedures based on…
This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation…
Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This…
The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…
We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…
We propose a class of flexible non-parametric tests for the presence of dependence between components of a random vector based on weighted Cram\'{e}r-von Mises functionals of the empirical copula process. The weights act as a tuning…
In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…
The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random…
We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of…
The replacement of indicator functions by integrated beta kernels in the definition of the empirical stable tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but…
This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing…
A key tool to carry out inference on the unknown copula when modeling a continuous multivariate distribution is a nonparametric estimator known as the empirical copula. One popular way of approximating its sampling distribution consists of…
Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations…
When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…
The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…
In the field of finance, insurance, and system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are…