Related papers: Deviation inequalities for sums of weakly dependen…

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…

Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on…

For a commutative non-autonomous dynamical system we show that topological transitivity of the non-autonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter…

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…

In this paper we analyze a system of N identical quantum particles in a weak-coupling regime. The time evolution of the Wigner transform of the one-particle reduced density matrix is represented by means of a perturbative series. The…

The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the…

In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…

There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…

We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are…

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…

The time derivative of a physical property often gives rise to another meaningful property. Since weak values provide empirical insights that cannot be derived from expectation values, this paper explores what physical properties can be…

The notes are an overview of part of the theory of pathwise weak solutions to two classes of scalar fully nonlinear first- and second-order degenerate parabolic partial differential equations with multiplicative rough time dependence, a…

We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation…

Irreversibility and acausality of a sub-system are established in exactly soluble harmonic models with reversible and causal dynamics. It is shown that initial conditions, imposed on some dynamical degrees of freedom may break time reversal…

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…

This paper provides extensions of the work on subsampling by Bertail et al. (2004) for strongly mixing case to weakly dependent case by application of the results of Doukhan and Louhichi (1999). We investigate properties of smooth and rough…

We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative…

We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…

We consider the problem of inference after model selection under weak assumptions in the time series setting. Even when the data are not independent, we show that sample splitting remains asymptotically valid as long as the process…