Related papers: A functional central limit theorem for the K-funct…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
We produce an estimate for the $K$-Bessel function $K_{r + i t}(y)$ with positive, real argument $y$ and of large complex order $r+it$ where $r$ is bounded and $t = y \sin \theta$ for a fixed parameter $0\leq \theta\leq \pi/2$ or $t= y…
Analytical formulae for functional differentiation under simultaneous K-conservation constraints, with K the integral of some function of the functional variable, are derived, making the proper account for the simultaneous conservation of…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
We propose new summary statistics for intensity-reweighted moment stationary point processes that generalise the well known J-, empty space, and nearest-neighbour distance distribution functions, represent them in terms of generating…
We study a class of integral functionals known as nonlocal perimeters, which, intuitively, express a weighted interaction between a set and its complement. The weight is provided by a positive kernel K, which might be singular. In the first…
Estimating entropy and mutual information consistently is important for many machine learning applications. The Kozachenko-Leonenko (KL) estimator (Kozachenko & Leonenko, 1987) is a widely used nonparametric estimator for the entropy of…
We consider the problem of optimally locating a given number $k$ of points in ${\mathbb R}^n$ for an integral cost function which takes into account two measures $\varphi^+$ and $\varphi^-$. The points represent for example new industrial…
We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.
In a functional setting, we propose two test statistics to highlight the Poisson nature of a Cox process when n copies of the process are available. Our approach involves a comparison of the empirical mean and the empirical variance of the…
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…
The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…
Many functionals of interest in statistics and machine learning can be written as minimizers of expected loss functions. Such functionals are called $M$-estimands, and can be estimated by $M$-estimators -- minimizers of empirical average…
We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…
This paper concerns space-sphere point processes, that is, point processes on the product space of $\mathbb R^d$ (the $d$-dimensional Euclidean space) and $\mathbb S^k$ (the $k$-dimen\-sional sphere). We consider specific classes of models…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
We define the minimum covariance determinant functionals for multivariate location and scatter through trimming functions and establish their existence at any multivariate distribution. We provide a precise characterization including a…
Let $X=\{X_n: n\in\mathbb{N}\}$ be the linear process defined by $X_n=\sum^{\infty}_{j=1} a_j\varepsilon_{n-j}$, where the coefficients $a_j=j^{-\beta}\ell(j)$ are constants with $\beta>0$ and $\ell$ a slowly varying function, and the…
New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…