Related papers: Asymptotic Stability of Empirical Processes and Re…
Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an approach to…
A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $\alpha-$divergence distances, is proposed. Sion's minimax theorem is…
Let $\Gamma$ be a relatively hyperbolic group and let $\mu$ be an admissible symmetric finitely supported probability measure on $\Gamma$. We extend Floyd-Ancona type inequalities up to the spectral radius of $\mu$. We then show that when…
For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n}…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We examine the stability of wireless networks whose users are distributed over a compact space. A subset of users is called {\it admissible} when their simultaneous activity obeys the prevailing interference constraints and, in each time…
The functional characterization of a measure, an essential but delicate aspect of Stein's method, is shown to be accessible for stable probability distributions on convex cones. This notion encompasses the usual stable distributions…
The normality assumption on data set is very restrictive approach for modelling. The generalized form of normal distribution, named as an exponential power (EP) distribution, and its scale mixture form have been considered extensively to…
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…
We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the…
For some discretely observed path of oscillating Brownian motion with level of self-organized criticality $\rho_0$, we prove in the infill asymptotics that the MLE is $n$-consistent, where $n$ denotes the sample size, and derive its limit…
In group sequential analysis, data is collected and analyzed in batches until pre-defined stopping criteria are met. Inference in the parametric setup typically relies on the limiting asymptotic multivariate normality of the repeatedly…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).…
We study the asymptotic hitting time $\tau^{(n)}$ of a family of Markov processes $X^{(n)}$ to a target set $G^{(n)}$ when the process starts from a trap defined by very general properties. We give an explicit description of the law of…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…
We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…
We introduce a new measure of robustness for statistical estimators, which we call \emph{empirical sensitivity}. An estimator $\hat \theta$ has bounded empirical sensitivity if, with high probability over a dataset $X = (X_1, \dots, X_n)…
We study stable like behaviour in first order theories without the independence property. We introduce generically stable measures, give characterizatiions, and show their ubiquity. We also introduce generic compact domination. We also…