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Related papers: Cram\'{e}r type large deviations for trimmed L-sta…

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The trimmed mean of $n$ scalar random variables from a distribution $P$ is the variant of the standard sample mean where the $k$ smallest and $k$ largest values in the sample are discarded for some parameter $k$. In this paper, we look at…

Statistics Theory · Mathematics 2025-01-08 Roberto I. Oliveira , Paulo Orenstein , Zoraida F. Rico

We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions…

Statistics Theory · Mathematics 2013-12-18 Liudas Giraitis , Hira L. Koul

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

We study inference using trimmed least squares (TLS) and trimmed least absolute deviations (TLAD) estimators of \citet{honore_trimmed_1992} in censored two-period panel-data models with fixed effects. We show that the published asymptotic…

Econometrics · Economics 2026-05-19 Denis Chetverikov , Jesper R. -V. ~Sørensen , Bo Honoré

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

The Koml\'os$\unicode{x2013}$Major$\unicode{x2013}$Tusn\'ady (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application has been hindered by a lack of practical constants.…

Statistics Theory · Mathematics 2026-05-19 Haoyu Ye , Morgane Austern

We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…

Statistics Theory · Mathematics 2015-07-07 Yu. Yu. Linke

This paper deals with the large deviations behavior of a stochastic process called thinned Levy process. This process appeared recently as a stochastic-process limit in the context of critical inhomogeneous random graphs. The process has a…

Probability · Mathematics 2014-04-08 Elie Aidekon , Remco van der Hofstad , Sandra Kliem , Johan S. H. van Leeuwaarden

When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (i) models should be designed to accommodate deductibles, policy limits, and coinsurance factors, (ii)…

Methodology · Statistics 2024-02-22 Chudamani Poudyal , Qian Zhao , Vytaras Brazauskas

Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime…

Information Theory · Computer Science 2015-06-11 Fabian Lim , Vladimir Marko Stojanovic

In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…

Optimization and Control · Mathematics 2016-12-20 Mihailo Stojnic

We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…

Probability · Mathematics 2017-10-10 E. Ostrovsky , L. Sirota

Let $X_1,X_2,...$ be independent random variables with zero means and finite variances, and let $S_n=\sum_{i=1}^nX_i$ and $V^2_n=\sum_{i=1}^nX^2_i$. A Cram\'{e}r type moderate deviation for the maximum of the self-normalized sums…

Statistics Theory · Mathematics 2013-07-24 Weidong Liu , Qi-Man Shao , Qiying Wang

In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space ({\em i.e.,} $d\gg n$) where the underlying parameter is assumed to be sparse. Specifically, we propose a…

Machine Learning · Statistics 2020-10-20 Di Wang , Xiangyu Guo , Shi Li , Jinhui Xu

Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random…

Probability · Mathematics 2020-07-07 Shankar Bhamidi , Amarjit Budhiraja , Paul Dupuis , Ruoyu Wu

In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…

Probability · Mathematics 2017-07-07 Yanghui Liu , Samy Tindel

The least trimmed squares (LTS) estimator is a renowned robust alternative to the classic least squares estimator and is popular in location, regression, machine learning, and AI literature. Many studies exist on LTS, including its…

Machine Learning · Statistics 2025-01-10 Yijun Zuo

A Cramer moderate deviation theorem for Hotelling's $T^2$-statistic is proved under a finite $(3+\delta)$th moment. The result is applied to large scale tests on the equality of mean vectors and is shown that the number of tests can be as…

Statistics Theory · Mathematics 2013-04-09 Weidong Liu , Qi-Man Shao

This paper proposes a robust and computationally efficient estimation framework for fitting parametric distributions based on trimmed L-moments. Trimmed L-moments extend classical L-moment theory by downweighting or excluding extreme order…

Methodology · Statistics 2025-05-16 Chudamani Poudyal , Qian Zhao , Hari Sitaula

Bagging is a useful method for large-scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for $M$-estimation problems but with massive datasets.…

Statistics Theory · Mathematics 2023-04-14 Yuan Gao , Riquan Zhang , Hansheng Wang