Related papers: Asymptotic Behaviour of Discretised Functionals of…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
Spatially distributed functional data are prevalent in many statistical applications such as meteorology, energy forecasting, census data, disease mapping, and neurological studies. Given their complex and high-dimensional nature,…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their…
We consider analysis of dependent functional data that are correlated because of a longitudinal-based design: each subject is observed at repeated time visits and for each visit we record a functional variable. We propose a novel…
The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these…
Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…
We consider a generalization of the weighted random ball model. The model is driven by a random Poisson measure with a product heavy tailed intensity measure. Such a model typically represents the transmission of a network of stations with…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate…
We present a brief survey of rigorous results on the asymptotic behavior of correlations between two local functions as the distance between their support diverges, concentrating on the Ising model on $\mathbb{Z}^d$ with finite-range…
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…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…
We extend generalized functional linear models under independence to a situation in which a functional covariate is related to a scalar response variable that exhibits spatial dependence-a complex yet prevalent phenomenon. For estimation,…
The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…