Related papers: Large Deviations Theorems in Nonparametric Regress…

Changes on temperature patterns, on a local scale, are perceived by individuals as the most direct indicators of global warming and climate change. As a specific example, for an Atlantic climate location, spring and fall seasons should…

Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…

Laws of large numbers, starting from certain nonequilibrium measures, have been shown for the integrated current across a bond, and a tagged particle in one-dimensional symmetric nearest-neighbor simple exclusion [Ann. Inst. Henri Poincare…

In this article, we consider the estimation of the structural change point in the nonparametric model with dependent observations. We introduce a maximum-CUSUM-estimation procedure, where the CUSUM statistic is constructed based on the…

In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…

In this paper, we study large deviation principles of nonlinear filtering for McKean-Vlasov stochastic differential equations. First of all, we establish the large deviation principle for the space-distribution dependent Zakai equation by a…

We describe large deviations for normalized multiple iterated sums and integrals of the form $\bbS_N^{(\nu)}(t)=N^{-\nu}\sum_{0\leq k_1<...<k_\nu\leq Nt}\xi(k_1)\otimes\cdots\otimes\xi(k_\nu)$, $t\in[0,T]$ and…

We study the Nadaraya-Watson (N-W) estimator for the drift function of two-sided reflected stochastic processes. We propose a discrete-type N-W estimator and a continuous-type N-W estimator based on the discretely observed processes and…

Let $i=1,\ldots,N$ index a simple random sample of units drawn from some large population. For each unit we observe the vector of regressors $X_{i}$ and, for each of the $N\left(N-1\right)$ ordered pairs of units, an outcome $Y_{ij}$. The…

In this paper, we establish a large deviation principle for stochastic evolution equations with reflection in an infinite dimensional ball. Weak convergence approach plays an important role.

The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…

We establish the large deviation principle for stochastic differential equations with averaging in the case when all coefficients of the fast component depend on the slow one, including diffusion.

This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…

This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…

We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…

Let X be a d dimensional vector of covariates and Y be the response variable. Under the nonparametric model Y = m(X) + {\sigma}(X) \in we develop an ANOVA-type test for the null hypothesis that a particular coordinate of X has no influence…

This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a…

We prove a large deviation principle for the largest eigenvalue of Wigner matrices without Gaussian tails, namely such that the distribution tails $\mathbb{P}( |X_{1,1}|>t)$ and $\mathbb{P}(|X_{1,2}|>t)$ behave like $e^{-bt^{\alpha}}$ and…

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…

Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large…