相关论文: On the tradeoff between almost sure error toleranc…

We consider the problem of detecting a general sparse mixture and obtain an explicit characterization of the phase transition under some conditions, generalizing the univariate results of Cai and Wu. Additionally, we provide a sufficient…

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index…

Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations…

Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…

From a recent geometric generalization of Thermodynamic Uncertainty Relations (TURs) we derive novel upper bounds on the nonlinear response of an observable of an arbitrary system undergoing a change of probabilistic state. Various…

An association rule is statistically significant, if it has a small probability to occur by chance. It is well-known that the traditional frequency-confidence framework does not produce statistically significant rules. It can both accept…

A generalized method of alternating resolvents was introduced by Boikanyo and Moro{\c s}anu as a way to approximate common zeros of two maximal monotone operators. In this paper we analyse the strong convergence of this algorithm under two…

We establish statistical limit theorems for equilibrium states of Axiom A diffeomorphisms, derived from the spectral gap of the Ruelle transfer operator established in Part I (Thiam2026a) and transferred to smooth dynamics through the…

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to…

For a Markov semigroup $P_t$ with invariant probability measure $\mu$, a constant $\ll>0$ is called a lower bound of the ultra-exponential convergence rate of $P_t$ to $\mu$, if there exists a constant $C\in (0,\infty)$ such that $$…

Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…

The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and…

The objective of the paper is to establish a computable upper bound for the almost sure convergence rate for a class of ratio consensus algorithms defined via column-stochastic matrices. Our result extends the works of Iutzeler et al.…

Thermodynamic uncertainty relations (TURs) express a fundamental tradeoff between the precision (inverse scaled variance) of any thermodynamic current by functionals of the average entropy production. Relying on purely variational…

This paper addresses the statistical problem of estimating the infinite-norm deviation from the empirical mean to the distribution mean for high-dimensional distributions on $\{0,1\}^d$, potentially with $d=\infty$. Unlike traditional…

We prove a martingale triangular array generalization of the Chow-Birnbaum-Marshall's inequality. The result is used to derive a strong law of large numbers for martingale triangular arrays whose rows are asymptotically stable in a certain…

Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…

The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…