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We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively…

Information Theory · Computer Science 2012-06-19 Swarnendu Kar , Pramod K. Varshney , Marimuthu Palaniswami

We study the convergence rate of the median estimator for affine matrix scrambled digital nets applied to integrands over the unit hypercube $[0, 1]^s$. By taking the median of $(2r-1)$ independent randomized quasi-Monte Carlo (RQMC)…

Numerical Analysis · Mathematics 2025-05-06 Yang Liu

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

The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class…

Machine Learning · Statistics 2025-06-23 Mikael Møller Høgsgaard , Andrea Paudice

A new test of normality based on a standardised empirical process is introduced in this article. The first step is to introduce a Cram\'er-von Mises type statistic with weights equal to the inverse of the standard normal density function…

Statistics Theory · Mathematics 2019-03-22 Juan Kalemkerian

In this paper, we derive an integral representation for the distribution of the number of types $K_n$ in the Ewens-Pitman model. Based on this representation, we also establish precise large deviations and precise moderate deviations for…

Probability · Mathematics 2025-12-16 Zhiqi Peng , Youzhou Zhou

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

Probability · Mathematics 2012-02-23 Florence Merlevède , Magda Peligrad , Emmanuel Rio

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

We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…

Data Structures and Algorithms · Computer Science 2024-11-25 Anindya De , Shivam Nadimpalli , Rocco A. Servedio

Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…

Machine Learning · Statistics 2024-11-27 Linda Chamakh , Zoltan Szabo

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of $\phi$-mixing sequences, contracting Markov chains, expanding maps…

Probability · Mathematics 2007-11-27 Jérôme Dedecker , Florence Merlevède , Magda Peligrad , Sergey Utev

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5,9]. However, one may wonder if this…

High Energy Physics - Lattice · Physics 2021-11-18 Tobias Rindlisbacher , Philippe de Forcrand

We prove strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type. This gives another application of a previous trimming result only proven for interval maps. In case of Markov measures we…

Dynamical Systems · Mathematics 2021-11-25 Marc Kesseböhmer , Tanja Schindler

We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…

Statistics Theory · Mathematics 2009-09-30 Olivier Catoni

We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…

Statistics Theory · Mathematics 2012-04-13 Thibault Espinasse , Paul Rochet

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…

Applications · Statistics 2019-11-20 Andrea Cappozzo , Francesca Greselin , Thomas Brendan Murphy

In this paper, we study self-normalized moderate deviations for degenerate { $U$}-statistics of order $2$. Let $\{X_i, i \geq 1\}$ be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form…

Probability · Mathematics 2025-01-08 Lin Ge , Hailin Sang , Qi-Man Shao

We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…

Probability · Mathematics 2007-05-23 Fabrice Gamboa , Li-Vang Lozada-Chang

We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…

Probability · Mathematics 2017-08-03 Xiequan Fan , Ion Grama , Quansheng Liu

When the individual studies assembled for a meta-analysis report means ($\mu_C$, $\mu_T$) for their treatment (T) and control (C) arms, but those data are on different scales or come from different instruments, the customary measure of…

Methodology · Statistics 2023-04-18 Elena Kulinskaya , David C. Hoaglin