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We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
We introduce two natural notions for the occupation measure of a function $V$ with finite variation. The first yields a signed measure, and the second a positive measure. By comparing two versions of the change-of-variables formula, we show…
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…
We extend methods of Ding and Smart from their breakthrough paper in 2020 which showed Anderson localization for certain random Schr\"odinger operators on $\ell^2(\mathbb{Z}^2)$ via a quantitative unique continuation principle and Wegner…
A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the…
Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
Here we develop a regularity theory for a polyconvex functional in $2\times2-$dimensional compressible finite elasticity. In particular, we consider energy minimizers/stationary points of the functional…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…
Elicitability is a property of $\mathbb{R}^k$-valued functionals defined on a set of distribution functions. These functionals represent statistical properties of a distribution, for instance its mean, variance, or median. They are called…
The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints.…
We consider additive functionals as a time and space-dependent function of a diffusion corresponding to nonhomogeneous uniformly elliptic divergence form operator. We show that if the function belongs to natural domain of strong solutions…
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…
This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…
Consider independent observations $(X_1,R_1)$, $(X_2,R_2)$, \ldots, $(X_n,R_n)$ with random or fixed ranks $R_i \in \{1,2,\ldots,k\}$, while conditional on $R_i = r$, the random variable $X_i$ has the same distribution as the $r$-th order…
One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional…
We formulate a criterion for the existence of an invariant measure for a Feller semigroup defined on a metric space with the e-property for bounded continuous functions and use it to prove the asymptotic stability of a semigroup satisfying…