相关论文: On Concentration and Revisited Large Deviations An…

We provide a general approach to obtain upper bounds for small deviations $ \mathbb{P}(\Vert y \Vert \le \epsilon)$ in different norms, namely the supremum and $\beta$- H\"older norms. The large class of processes $y$ under consideration…

In this paper, we study various models for random combinatorial partitions using large deviation analysis for diverging scale of the reference process. Scaling limits of similar models have been studied recently \cite{FSa,FSb} going back to…

While standard statistical inference techniques and machine learning generalization bounds assume that tests are run on data selected independently of the hypotheses, practical data analysis and machine learning are usually iterative and…

The randomized $p$-value, (nonrandomized) mid-$p$-value and abstract randomized $p$-value have all been recommended for testing a null hypothesis whenever the test statistic has a discrete distribution. This paper provides a unifying…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…

In this paper we present a simple partitioning based technique to refine the statistical analysis of classification algorithms. The core of our idea is to divide the input space into two parts such that the first part contains a suitable…

The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the…

For sufficiently smooth bounded plane domains, the equivalence between the inequalities of Babu{\v s}ka --Aziz for right inverses of the divergence and of Friedrichs on conjugate harmonic functions was shown by Horgan and Payne in 1983 [7].…

The present paper establishes convolution theorems for regular estimators when the limit experiment is non-Gaussian or of infnite dimension with sparse parameter space. Applications are given for Gaussian shift experiments of infnite…

We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…

We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which…

The improved method of intermittent data analysis is proposed. It exploits, in addition to the standard density moments, the information on the bin-bin correlations, observed in the data and expressed in terms of the density correlators.…

We apply Lindeberg's method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate deviation principles for martingales as well as for random…

Stochastic estimators are fundamental to large-scale optimization, where population quantities must be inferred from noisy oracle observations. Although influential methods such as momentum, SPIDER, STORM, and PAGE have been highly…

We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…

In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let $X_1,X_2,\ldots$ be a sequence of independent identically distributed Bernoulli random variables, with expectation $p$ under $\mathcal{H}_0$…

This is a research endeavor in two parts. We study a class of balanced urn schemes on balls of two colours (say white and black). At each drawing, a sample of size $m\ge 1$ is drawn from the urn, and ball addition rules are applied. We…

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…