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Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…

Probability · Mathematics 2016-08-11 V. Yu. Korolev , A. V. Dorofeeva

Integrated autoregressive conditional duration (ACD) models serve as natural counterparts to the well-known integrated GARCH models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is challenging and…

Econometrics · Economics 2025-05-12 Giuseppe Cavaliere , Thomas Mikosch , Anders Rahbek , Frederik Vilandt

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and…

Statistics Theory · Mathematics 2015-01-28 Jinyuan Chang , Song Xi Chen , Xiaohong Chen

Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…

Probability · Mathematics 2007-05-23 Victor H. de la Pena , Michael J. Klass , Tze Leung Lai

We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…

Econometrics · Economics 2026-01-27 Xuan Leng , Jiaming Mao , Yutao Sun

In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong $L^p$-convergence version and a strongly quasi sure…

Probability · Mathematics 2019-03-15 Ze-Chun Hu , Ning-Hua Liu , Ting Ma

The problem of sequentially detecting an abrupt change in a sequence of independent and identically distributed (IID) random variables is addressed. Whereas previous approaches assume a known probability density function (PDF) at the start…

Statistics Theory · Mathematics 2017-12-11 James Falt , Steven D. Blostein

A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…

Information Theory · Computer Science 2007-11-15 Gil I. Shamir

In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of…

Machine Learning · Statistics 2012-02-20 Chao Zhang , Dacheng Tao

We give error estimates in Peng's central limit theorem for not necessarily nondegenerate case. The exposition uses the language of the classical probability theory instead of the language of the theory of sublinear expectations. We only…

Probability · Mathematics 2018-07-02 N. V. Krylov

We revisit sequential outlier hypothesis testing and derive bounds on achievable exponents when both the nominal and anomalous distributions are unknown. The task of outlier hypothesis testing is to identify the set of outliers that are…

Information Theory · Computer Science 2025-04-24 Jun Diao , Lin Zhou

A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: Given a sequence of random variables $X_1,\dots,X_n$ drawn independently from a distribution $F$,…

Data Structures and Algorithms · Computer Science 2021-04-08 José R. Correa , Paul Dütting , Felix Fischer , Kevin Schewior

We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional…

Information Theory · Computer Science 2019-05-21 Abhik Ghosh

Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…

Statistics Theory · Mathematics 2026-01-21 Vladimir Vovk

We prove the central limit theorem (CLT) for a sequence of independent zero-mean random variables $\xi_j$, perturbed by predictable multiplicative factors $\lambda_j$ with values in intervals $[\underline\lambda_j,\overline\lambda_j]$. It…

Probability · Mathematics 2015-08-31 Dmitry B. Rokhlin

We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions include an appropriate negative drift together with a…

Probability · Mathematics 2011-07-26 Arnab Ganguly , Debasish Chatterjee , John Lygeros , Heinz Koeppl

We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…

Methodology · Statistics 2024-11-22 Tommaso Lando Idir Arab , Paulo Eduardo Oliveira

We study the Hsu-Robbins-Erd\"os theorem to the case when all moments under sub-linear expectations exist, but the moment generating function does not, viz, we suppose that…

Probability · Mathematics 2025-08-27 Xu Mingzhou , Yang Jinjin

Sublinear expectations for uncertain processes have received a lot of attention recently, particularly methods to extend a downward-continuous sublinear expectation on the bounded finitary functions to one on the non-finitary functions. In…

Probability · Mathematics 2023-05-05 Alexander Erreygers

In this paper, we propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations (PIDEs) which characterize the nonlinear $\alpha$-stable L\'{e}vy processes under sublinear…

Probability · Mathematics 2024-06-12 Mingshang Hu , Lianzi Jiang , Gechun Liang