Related papers: A note on extreme values and kernel estimators of …
In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We…
This paper deals with parameter estimation from extreme measurements. While being a special case of parameter estimation from partial data, in scenarios where only one sample from a given set of K measurements can be extracted, choosing…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type…
The extremal process of a branching random walk is the point measure recording the position of particles alive at time $n$, shifted around the expected position of the minimal position. Madaule proved that this point measure converges, as…
In this paper, we study the statistical properties of kernel $k$-means and obtain a nearly optimal excess clustering risk bound, substantially improving the state-of-art bounds in the existing clustering risk analyses. We further analyze…
A random geometric graph $G(\mathcal{X}_n, r_n)$ is formed by taking a binomial process $\mathcal{X}_n$ as the set of vertices and joining any two distinct points with an edge if they lie within distance $r_n$ of each other. We investigate…
U-max statistics were introduced by Lao and Mayer in 2008. Instead of averaging the kernel over all possible subsets of the original sample, they considered the maximum of the kernel. Such statistics are natural in stochastic geometry.…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
Estimation of extreme quantile regions, spaces in which future extreme events can occur with a given low probability, even beyond the range of the observed data, is an important task in the analysis of extremes. Existing methods to estimate…
We study the asymptotic edge statistics of the Gaussian $\beta$-ensemble, a collection of $n$ particles, as the inverse temperature $\beta$ tends to zero as $n$ tends to infinity. In a certain decay regime of $\beta$, the associated extreme…
A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme…
Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…
Several two-boundary problems are solved for a special L\'{e}vy process: the Poisson process with an exponential component. The jumps of this process are controlled by a homogeneous Poisson process, the positive jump size distribution is…
We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme…
We consider continuous time simple random walks with arbitrary speed measure $\theta$ on infinite weighted graphs. Write $p_t(x,y)$ for the heat kernel of this process. Given on-diagonal upper bounds for the heat kernel at two points…
In this paper, quantitative central limit theorems for $U$-statistics on the $q$-dimensional torus defined in the framework of the two-sample problem for Poisson processes are derived. In particular, the $U$-statistics are built over tight…
Probability boxes, also known as $p$-boxes, correspond to sets of probability distributions bounded by a pair of distribution functions. They fall into the class of models known as imprecise probabilities. One of the central questions…
We consider both the infinite-volume discrete Gaussian Free Field (DGFF) and the DGFF with zero boundary conditions outside a finite box in dimension larger or equal to 3. We show that the associated extremal process converges to a Poisson…