Related papers: Correlated Binomial Process

Correlated component analysis as proposed by Dmochowski et al. (2012) is a tool for investigating brain process similarity in the responses to multiple views of a given stimulus. Correlated components are identified under the assumption…

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional…

We study Rademacher processes where the coefficients are functions evaluated at fixed, but arbitrary covariables. Specifically, we assume the function class under consideration to be parametrized by the standard cocube in l dimensions and…

Consider a polynomial of large degree n whose coefficients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that such a polynomial has exactly k real zeros…

Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This…

Almost 10 years ago, Impagliazzo and Kabanets (2010) gave a new combinatorial proof of Chernoff's bound for sums of bounded independent random variables. Unlike previous methods, their proof is constructive. This means that it provides an…

The question how the extremal values of a stochastic process achieved on different time intervals are correlated to each other has been discussed within the last few years on examples of the running maximum of a Brownian motion, of a…

We establish a multivariate empirical process central limit theorem for stationary $\R^d$-valued stochastic processes $(X_i)_{i\geq 1}$ under very weak conditions concerning the dependence structure of the process. As an application we can…

We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of…

It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. Most results towards an affirmative answer have so far been restricted to almost sure…

The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on…

We introduce two new concepts designed for the study of empirical processes. First, we introduce a new Orlicz norm which we call the Bernstein-Orlicz norm. This new norm interpolates sub-Gaussian and sub-exponential tail behavior. In…

This paper is motivated by relations between association and independence of random variables. It is well-known that for real random variables independence implies association in the sense of Esary, Proschan and Walkup, while for random…

The century old extremal problem, solved by Carath\'eodory and Fej\'er, concerns a nonnegative trigonometric polynomial normalized by a0 = 1, and the quantity to be maximized is the coefficient a1. In the complex exponential form, the…

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…

G-Brownian motion has a very rich and interesting new structure which nontrivially generalizes the classical one. Its quadratic variation process is also a continuous process with independent and stationary increments. We prove a…

In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is \v{C}ech cohomology. We show in particular that the \v{C}ech cohomology groups of the…

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…