Related papers: Self-Normalized Concentration Inequalities of Marg…
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…
In this paper, we aim at characterizing generalized functionals of discrete-time normal martingales. Let $M=(M_n)_{n\in \mathbb{N}}$ be a discrete-time normal martingale that has the chaotic representation property. We first construct…
Novel significance tests are proposed for the quite general additive concurrent model formulation without the need of model, error structure preliminary estimation or the use of tuning parameters. Making use of the martingale difference…
We study branching Markov chains on a countable state space (space of types) $\mathscr{X}$, with the focus on the qualitative aspects of the limit behaviour of the evolving empirical population distributions. No conditions are imposed on…
We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…
While attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations not present in block-randomized experiments with multiple treated and control individuals in…
New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The…
Analysis of three-way data is becoming ever more prevalent in the literature, especially in the area of clustering and classification. Real data, including real three-way data, are often contaminated by potential outlying observations.…
We obtain a condition for the $L^q$-convergence of martingales generated by random multiplicative cascade measures for $q>1$ without any self-similarity requirements on the cascades.
We consider a diffusion processes $\{ X_t \}$ on an interval in the natural scale. Some results are known under which $\{ X_t \}$ is a martingale, and we give simple and analytic proofs for them.
We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…
This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A…
Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multi-centre trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal…
Recently, a new approach in the fine analysis of stochastic processes sample paths has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of…
Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
We characterise the unbiasedness of the score function, viewed as an inference function for a class of finite mixture models. The models studied represent the situation where there is a stratification of the observations in a finite number…
We show that for a convex function the following, rather modest conditions, are equivalent to monotonicity under local operations and classical communication. The conditions are: 1)invariance under local unitaries, 2) invariance under…
The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…
We establish an Azuma type inequality under a Lipshitz condition for martingales in the framework of noncommutative probability spaces and apply it to deduce a noncommutative Heoffding inequality as well as a noncommutative McDiarmid type…