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Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential…

Probability · Mathematics 2016-10-25 Christophe Cuny , Jérôme Dedecker , Florence Merlevède

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Statistics Theory · Mathematics 2026-02-10 Jiming Jiang , Matt P. Wand , Swarnadip Ghosh

We obtain error rates for large deviations of sums of i.i.d. random variables in, a particular case, of the domain of a non-symmetric infinite mean $\alpha=1$-stable law. The focus of this work is on the method of proof via analytic…

Probability · Mathematics 2025-06-17 Jonny Imbierski , Dalia Terhesiu

This is basically a polished presentation for Sections 1,2 of arXiv:0801.1050. The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and…

Probability · Mathematics 2016-12-28 Boris Tsirelson

In an influential critique of empirical practice, Freedman (2008) showed that the linear regression estimator was biased for the analysis of randomized controlled trials under the randomization model. Under Freedman's assumptions, we derive…

Methodology · Statistics 2021-10-26 Haoge Chang , Joel Middleton , P. M. Aronow

Asymptotics deviation probabilities of the sum S n = X 1 + $\times$ $\times$ $\times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated , in particular when X 1 is not…

Probability · Mathematics 2020-10-20 Thierry Klein , Agnès Lagnoux , Pierre Petit

The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…

Information Theory · Computer Science 2024-05-30 Valentinian Lungu , Ioannis Kontoyiannis

The aim of this paper is to get asymptotic deviation bounds via a Large Deviation Principle (LDP) for cumulative processes also known as compound renewal processes or renewal-reward processes. These processes cumulate independent random…

Probability · Mathematics 2023-06-21 Patrick Cattiaux , Laetitia Colombani , Manon Costa

For a multivariate random walk with i.i.d. jumps satisfying the Cramer moment condition and having a mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant…

Probability · Mathematics 2019-05-09 Yuqing Pan , Konstantin Borovkov

The aim of this short article is to convey the basic idea of the original paper [3], without going into too much detail, about how to derive sharp asymptotics of the gyration radius for random walk, self-avoiding walk and oriented…

Probability · Mathematics 2009-12-31 Akira Sakai

We study the statistics of the number of real eigenvalues in the elliptic deformation of the real Ginibre ensemble. As the matrix dimension grows, the law of large numbers and the central limit theorem for the number of real eigenvalues are…

Probability · Mathematics 2025-11-26 Sung-Soo Byun , Jonas Jalowy , Yong-Woo Lee , Grégory Schehr

We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing…

Probability · Mathematics 2012-05-31 Nikolaus Schweizer

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

Optimization and Control · Mathematics 2018-09-24 Atiye Alaeddini , Siavash Alemzadeh , Afshin Mesbahi , Mehran Mesbahi

The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the…

Methodology · Statistics 2014-06-18 Johan Segers

In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…

Probability · Mathematics 2009-09-29 Philippe Barbe

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential…

Numerical Analysis · Mathematics 2018-02-16 Kristian Debrabant , Jens Lang

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

Statistics Theory · Mathematics 2025-04-08 Jana Gauss , Thomas Nagler

Record numbers are basic statistics in random walks, whose deviation principles are not very clear so far. In this paper, the asymptotic probabilities of large and moderate deviations for numbers of weak records in right continuous or left…

Probability · Mathematics 2023-01-10 Yuqiang Li , Qiang Yao

Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the…

Statistics Theory · Mathematics 2017-12-12 Matias D. Cattaneo , Michael Jansson , Whitney K. Newey

We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…

chao-dyn · Physics 2008-02-03 J. Bricmont , A. Kupiainen , G. Lin