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This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these…
The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.
Let $\{P_{\theta}:\theta \in {\mathbb R}^d\}$ be a log-concave location family with $P_{\theta}(dx)=e^{-V(x-\theta)}dx,$ where $V:{\mathbb R}^d\mapsto {\mathbb R}$ is a known convex function and let $X_1,\dots, X_n$ be i.i.d. r.v. sampled…
We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…
Variable Muckenhoupt weights are considered in variable exponent Lebesgue spaces. Applications are given for polynomial approximation in these spaces. Boundedness of averaging operator is proved to gain a transference result. Almost all…
As a part of our works on effective properties of probability distributions, we deal with the corresponding characteristic functions. A sequence of probability distributions is computable if and only if the corresponding sequence of…
We study the properties of the set of marginal distributions of infinite translation-invariant systems in the 2D square lattice. In cases where the local variables can only take a small number $d$ of possible values, we completely solve the…
Under the separability assumption on the augmented density, a distribution function can be always constructed for a spherical population with the specified density and anisotropy profile. Then, a question arises, under what conditions the…
For arbitrary linear time-invariant systems, the existence of a strong functional observer is investigated. Such observer determines, from the available measurement on the plant, an estimate of a function of the state and the input. This…
We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…
We study the quasi-stationary behavior of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka-Volterra birth and death processes and Feller diffusions with…
We deal with an inverse elastic scattering problem for the shape determination of a rigid scatterer in the time-harmonic regime. We prove a local stability estimate of log log type for the identification of a scatterer by a single far-field…
We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and…
Many practical problems are related to the pointwise estimation of dis- tribution functions when data contains measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control,…
We define data transformations that leave certain classes of distributions invariant, while acting in a specific manner upon the parameters of the said distributions. It is shown that under such transformations the maximum likelihood…
We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions…
A common assumption when sampling $p$-dimensional observations from $K$ distinct group is the equality of the covariance matrices. In this paper, we propose two penalized $M$-estimation approaches for the estimation of the covariance or…
The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…