Related papers: The delta method for analytic functions of random …
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor…
Based on the here developed functional analytic machinery we extend the theory of operator sampling and identification to apply to operators with stochastic spreading functions. We prove that identification with a delta train signal is…
We develop a framework of canonical correlation analysis for distribution-valued functional data within the geometry of Wasserstein spaces. Specifically, we formulate an intrinsic concept of correlation between random distributions, propose…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
Randomization tests are based on a re-randomization of existing data to gain data-dependent critical values that lead to exact hypothesis tests under special circumstances. However, it is not always possible to re-randomize data in…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted…
If $T$ is a (densely defined) self-adjoint operator acting on a complex Hilbert space $\mathcal{H}$ and $I$ stands for the identity operator, we introduce the delta function operator $\lambda \mapsto \delta \left(\lambda I-T\right) $ at…
In the present paper, we study the analyticity of the leftmost eigenvalue of the linear elliptic partial differential operator with random coefficient and analyze the convergence rate of the quasi-Monte Carlo method for approximation of the…
We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
This paper investigates the asymptotic and non-asymptotic behavior of the quantized primal dual algorithm in network utility maximization problems, in which a group of agents maximize the sum of their individual concave objective functions…
In many situations, when dealing with several populations, equality of the covariance operators is assumed. An important issue is to study if this assumption holds before making other inferences. In this paper, we develop a test for…
The Dirac delta function is widely used in many areas of physics and mathematics. Here we consider the generalization of a Dirac delta function to allow the use of complex arguments. We show that the properties of a generalized delta…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
We aim to analyze the relation between two random vectors that may potentially have both different number of attributes as well as realizations, and which may even not have a joint distribution. This problem arises in many practical…
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…