Related papers: Weak convergence of empirical copula processes ind…
For a measure preserving dynamical system $(\mathcal{X},f, \mu)$, we consider the time series of maxima $M_n=\max\{X_1,\ldots,X_n\}$ associated to the process $X_n=\phi(f^{n-1}(x))$ generated by the dynamical system for some observable…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
Regression analyses based on transformations of cumulative incidence functions are often adopted when modeling and testing for treatment effects in clinical trial settings involving competing and semi-competing risks. Common frameworks…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…
If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…
We study the behavior of bivariate empirical copula process $\mathbb{G}_n(\cdot,\cdot)$ on pavements $[0,k_n/n]^2$ of $[0,1]^2,$ where $k_n$ is a sequence of positive constants fulfilling some conditions. We provide a upper bound for the…
This study outlines a comprehensive methodology utilizing copulas to discern inconsistencies in the behavior exhibited by pairs of financial assets. It introduces a robust approach to establishing the interrelationship between the returns…
We are studying the problems of modeling and inference for multivariate count time series data with Poisson marginals. The focus is on linear and log-linear models. For studying the properties of such processes we develop a novel conceptual…
We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical…
In this note, we provide upper bounds on the expectation of the supremum of empirical processes indexed by H\"older classes of any smoothness and for any distribution supported on a bounded set in $\mathbb R^d$. These results can be…
Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process.…
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts…
We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be…
Let $(X_k)_{k\geq1}$ be a Gaussian long-range dependent process with $EX_1=0$, $EX_1^2=1$ and covariance function $r(k)=k^{-D}L(k)$. For any measurable function $G$ let $(Y_k)_{k\geq1}=(G(X_k))_{k\geq1}$. We study the asymptotic behaviour…
The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings.…
This article deals with the lower compactness property of a sequence of integrands and the use of this key notion in various domains: convergence theory, optimal control, non-smooth analysis. First about the interchange of the weak…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…