Related papers: Limit Theorems in Mallows Distance for Processes w…
In this paper, we study the distribution of the minimal distance (in the Hamming metric) of a random linear code of dimension $k$ in $\mathbb{F}_q^n$. We provide quantitative estimates showing that the distribution function of the minimal…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting…
In this article, we introduce \textit{Mallows processes}, defined to be continuous-time c\`adl\`ag processes with Mallows distributed marginals. We show that such processes exist and that they can be restricted to have certain natural…
We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of…
This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…
This article gives a new proof that fully connected neural networks with random weights and biases converge to Gaussian processes in the regime where the input dimension, output dimension, and depth are kept fixed, while the hidden layer…
Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an…
Under certain mild conditions, limit theorems for additive functionals of some $d$-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions,…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
The stochastic properties of variables whose addition leads to $q$-Gaussian distributions $G_q(x)=[1+(q-1)x^2]_+^{1/(1-q)}$ (with $q\in\mathbb{R}$ and where $[f(x)]_+=max\{f(x),0\}$) as limit law for a large number of terms are…
We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of…
This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…
The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning principle for thin sets). Applications to…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
The Mallows measure is a probability measure on $S_n$ where the probability of a permutation $\pi$ is proportional to $q^{l(\pi)}$ with $q > 0$ being a parameter and $l(\pi)$ the number of inversions in $\pi$. We prove a weak law of large…