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We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…

Probability · Mathematics 2022-05-27 Xiao Fang , Yuta Koike

This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…

Probability · Mathematics 2023-04-13 Matthias Schulte , Christoph Thaele

The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…

Probability · Mathematics 2012-09-28 Hanna Doering , Peter Eichelsbacher

In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed $L$-statistics and we apply it to the Cram\'{e}r type large deviation problem. Our results can be compared with ones in Callaert et al.(1982)…

Probability · Mathematics 2019-04-23 Nadezhda Gribkova

In this paper, Cram\'{e}r type moderate deviations for the maximum of the periodogram and its studentized version are derived. The results are then applied to a simultaneous testing problem in gene expression time series. It is shown that…

Probability · Mathematics 2009-08-11 Weidong Liu , Qi Man Shao

In this article, we discuss the sharp moderate and large deviations between the quantiles of population and the quantiles of samples. Cram\'{e}r type moderate deviations and Bahadur-Rao type large deviations are established with some mild…

Statistics Theory · Mathematics 2023-10-03 Xiequan Fan

The empirical mean of $n$ independent and identically distributed (i.i.d.) random variables $(X_1,\dots,X_n)$ can be viewed as a suitably normalized scalar projection of the $n$-dimensional random vector $X^{(n)}\doteq(X_1,\dots,X_n)$ in…

Probability · Mathematics 2015-10-07 Nina Gantert , Steven Soojin Kim , Kavita Ramanan

Let $\{Z_n, n\geq 0\}$ be a supercritical branching process in an independent and identically distributed random environment. We prove Cram\'{e}r moderate deviations and Berry-Esseen bounds for $\ln (Z_{n+n_0}/Z_{n_0})$ % under the annealed…

Probability · Mathematics 2020-02-04 Xiequan Fan , Haijuan Hu , Quansheng Liu

This paper investigates weighted approximations for studentized $U$-statistics type processes, both with symmetric and antisymmetric kernels, only under the assumption that the distribution of the projection variate is in the domain of…

Probability · Mathematics 2007-11-12 Miklós Csörgő , Barbara Szyszkowicz , Qiying Wang

A uniform in probability approximation is established for Studentized processes of non degenerate U-statistics of order m greater or equal to 2 in terms of a standard Wiener process. The classical condition that the second moment of kernel…

Probability · Mathematics 2009-06-30 Masoud M. Nasari

Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…

Probability · Mathematics 2009-09-29 Victor H. de la Peña , Michael J. Klass , Tze Leung Lai

For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…

Probability · Mathematics 2015-04-14 S. G. Bobkov , G. P. Chistyakov , F. Götze

Let $(Z_n)_{n\geq0}$ be a supercritical Galton-Watson process. Consider the Lotka-Nagaev estimator for the offspring mean. In this paper, we establish self-normalized Cram\'{e}r type moderate deviations and Berry-Esseen's bounds for the…

Probability · Mathematics 2023-10-03 Xiequan Fan , Qi-Man Shao

We consider a stochastic differential equation and its Euler-Maruyama (EM) scheme, under some appropriate conditions, they both admit a unique invariant measure, denoted by $\pi$ and $\pi_\eta$ respectively ($\eta$ is the step size of the…

Probability · Mathematics 2021-09-09 Jianya Lu , Yuzhen Tan , Lihu Xu

Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$, where $(g_n)_{n\geq 1}$ is a sequence of independent and identically distributed random elements with law $\mu$ on the general linear group ${\rm GL}(V)$ with $V=\mathbb R^d$.…

Probability · Mathematics 2022-09-13 Hui Xiao , Ion Grama , Quansheng Liu

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

Probability · Mathematics 2024-11-20 Rita Giuliano , Claudio Macci , Barbara Pacchiarotti

This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…

Signal Processing · Electrical Eng. & Systems 2018-04-30 Antonio Moschitta , Johan Schoukens , Paolo Carbone

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate…

Probability · Mathematics 2020-11-05 Nikolai Leonenko , Claudio Macci , Barbara Pacchiarotti

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

Probability · Mathematics 2026-05-25 Giampaolo Cristadoro , Gaia Pozzoli

In this paper, we consider moderate deviations for Good's coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good's coverage estimator are established. The results are also applied…

Statistics Theory · Mathematics 2013-05-10 Fuqing Gao