Related papers: A note on extreme values and kernel estimators of …
We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of observations. Motivated by this problem, in this contribution we first investigate the extremes of Gaussian fields…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of…
In this paper we derive quantitative boundary H\"older estimates, with explicit constants, for the inhomogeneous Poisson problem in a bounded open set $D\subset \mathbb{R}^d$. Our approach has two main steps: firstly, we consider an…
We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters,…
We consider the problem of estimating the support of a measure from a finite, independent, sample. The estimators which are considered are constructed based on the empirical Christoffel function. Such estimators have been proposed for the…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Let $X=\{X_n: n\in \mathbb{N}\}$ be a linear process with bounded probability density function $f(x)$. Under certain conditions, we use the kernel estimator \[ \frac{2}{n(n-1)h_n} \sum_{1\le i<j\le n}K\Big(\frac{X_i-X_j}{h_n}\Big) \] to…
We apply the Stein-Chen method to problems from extreme value theory. On the one hand, the Stein-Chen method for Poisson approximation allows us to obtain bounds on the Kolmogorov distance between the law of the maximum of i.i.d. random…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
We present a procedure for calculating an upper limit on the number of signal events which incorporates the Poisson uncertainty in the background, estimated from control regions of one or two dimensions. For small number of signal events,…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse…
This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…
Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
In this note, we provide upper bounds on the expectation of the supremum of empirical processes indexed by H\"older classes of any smoothness and for any distribution supported on a bounded set in $\mathbb R^d$. These results can be…
We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \mathscr Q(z)}$ depending on a potential $\mathscr Q:\mathbb C^d\to\mathbb R$. We use these kernels to construct determinantal point processes on…
We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…