Related papers: A Framework for Asymptotic Limit Problems of Proba…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness…
We study the asymptotics of the moments of arithmetic functions that have a limit distribution, not necessarily normal, defined on a subset of the natural series that satisfies certain requirements. Several assertions are proved on…
Given a countably infinite group $G$ acting on some space $X$, an increasing family of finite subsets $G_n$ and $x\in X$, a natural question to ask is what asymptotical distribution the sets $G_nx$ form. More formally, we define for a…
The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
The nonparametric problem of detecting existence of an anomalous interval over a one dimensional line network is studied. Nodes corresponding to an anomalous interval (if exists) receive samples generated by a distribution q, which is…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various…
The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit…
We describe a general probabilistic framework to address a variety of Frechet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in $d$-dimensional Euclidean space between given start and…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…
We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…
We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime square and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…