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Related papers: Nonstandard Convergence Gives Bounds on Jumps

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A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…

Probability · Mathematics 2019-03-26 Viktor Bengs , Hajo Holzmann

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…

Statistics Theory · Mathematics 2016-11-14 Teo Sharia , Lei Zhong

Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…

Combinatorics · Mathematics 2021-09-01 Hiêp Hàn , Marcos Kiwi , Matías Pavez-Signé

Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…

Quantum Physics · Physics 2014-07-17 M. M. Taddei

We prove the uniform oscillation and jump inequalities for the polynomial ergodic averages modeled over multi-dimensional subset of primes. These inequalities provide endpoints for the $r$-variational estimates obtained by Trojan…

Dynamical Systems · Mathematics 2023-03-16 Nathan Mehlhop , Wojciech Słomian

Based on T.Tao's result of norm convergence of multiple ergodic averages for commut-ing transformation, we obtain there is a subsequence which converges almost everywhere. Meanwhile, the ergodic behaviour, which the time average is equal to…

Dynamical Systems · Mathematics 2021-12-07 Xia Pan , Zuohuan Zheng , Zhe Zhou

When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…

Probability · Mathematics 2019-05-01 Miles E. Lopes

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

Probability · Mathematics 2025-01-29 Alexander Shmyrov , Vasily Shmyrov

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

Econometrics · Economics 2025-09-16 Jiatong Li , Hongqiang Yan

The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a…

Probability · Mathematics 2017-04-10 Nicolas Champagnat , Denis Villemonais

For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of nonnegative random variables where $\max[\min(X_{n} - s,t),0]$, $t > s \geqslant 0$, satisfy a moment inequality, sufficient conditions are given under which $\sum_{k=1}^n (X_k - \mathbb{E}…

Probability · Mathematics 2020-11-23 João Lita da Silva

We calculate explicit speeds for random walks in uniform degenerate random environments. For certain non-uniform random environments, we calculate speeds that are non-monotone.

Probability · Mathematics 2013-04-30 Mark Holmes , Thomas S. Salisbury

We give lower bounds on the maximum possible girth of an $r$-uniform, $d$-regular hypergraph with at most $n$ vertices, using the definition of a hypergraph cycle due to Berge. These differ from the trivial upper bound by an absolute…

Combinatorics · Mathematics 2017-07-14 David Ellis , Nathan Linial

For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…

Methodology · Statistics 2012-12-06 Xin Liao , Zuoxiang Peng , Saralees Nadarajah , Xiaoqian Wang

We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed…

Statistical Mechanics · Physics 2023-03-24 Andreas Dechant , Jerome Garnier-Brun , Shin-ichi Sasa

We derive a consistency result, in the $L_1$-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order $p(\geq 1)$, we obtain…

Statistics Theory · Mathematics 2021-12-30 Alexander Dürre , Davy Paindaveine

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

Statistics Theory · Mathematics 2021-11-30 Morgane Austern , Peter Orbanz

In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus, even in the…

Probability · Mathematics 2012-06-01 J. Dedecker , F. Merlevède , F. Pène

In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…

Statistics Theory · Mathematics 2013-11-05 Xinjia Chen

The problem of sequential anomaly detection and identification is considered, where multiple data sources are simultaneously monitored and the goal is to identify in real time those, if any, that exhibit ``anomalous" statistical behavior.…

Statistics Theory · Mathematics 2024-12-09 Aristomenis Tsopelakos , Georgios Fellouris
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