Related papers: The Central Limit Theorem for LS Estimator in Simp…
In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…
In our previous paper \cite{FTD1}, we derived the almost sure convergence of the global density of eigenvalues of random matrices of the SYK model. In this paper, we will prove the central limit theorem for the linear statistic of…
In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal…
The second and third-named authors (arXiv:1705.04115) established a Central Limit Theorem for the error term in the Sato-Tate law for families of modular forms. This method was adapted to families of elliptic curves in by the first and…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems…
This paper investigates the finite-sample prediction risk of the high-dimensional least squares estimator. We derive the central limit theorem for the prediction risk when both the sample size and the number of features tend to infinity.…
A Central Limit Theorem for linear combinations of iterates of an inner function is proved. The main technical tool is Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures.
We study the Central Limit Theorem (CLT) in the so-called hybrid Lebesgue-continuous spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT…
This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding…
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…
M-estimators for Generalized Linear Models are considered under minimal assumptions. Under these preliminaries, strong convergence of the estimators are discussed and an expansion of the estimating operators are given in the non-i.i.d. case…
We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
We derive Esseen type bounds of the remainder in a combinatorial central limit theorem for independent random variables without third moments.
The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…