Yandi Shen, Fang Han, Daniela Witten
We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of expansion is new and useful for handling many notorious classes of kernels.
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We extend the dimension free Talagrand inequalities for convex distance \cite{talagrand:1995} using an extension of Marton's weak transport \cite{marton:1996a} to other metrics than the Hamming distance. We study the dual form of these weak transport inequalities for the euclidian norm and prove that it implies sub-gaussianity and convex Poincaré inequality \cite{bobkov:gotze:1999a}. We obtain new weak transport inequalities for non products measures extending the results of Samson in \cite{samson:2000}. Many examples are provided to show that the euclidian norm is an appropriate metric for cl…
Exponential inequalities for empirical unbounded context trees
在本文中，我们获得了非一致指数上界的收敛速率的算法上下文的版本，当底层树不一定有界。Context算法是一个著名的估计变长马尔可夫链上下文树的工具。作为指数界的结果，我们得到一个强一致性结果。我们以这种方式推广了该领域的几个先前的结果。
Exponential inequalities for self-normalized martingales with applications
我们提出了几个自正规化鞅的指数不等式，类似于De la Peña所建立的。重点是引入了左重或右重随机变量的新概念。还提供了与线性回归、自回归和分支过程相关的应用。
Motivated by problems arising in random sampling of trigonometric polynomials, we derive exponential inequalities for the operator norm of the difference between the sample second moment matrix $n^{-1}U^*U$ and its expectation where $U$ is a complex random $n\times D$ matrix with independent rows. These results immediately imply deviation inequalities for the largest (smallest) eigenvalues of the sample second moment matrix, which in turn lead to results on the condition number of the sample second moment matrix. We also show that trigonometric polynomials in several variables can be learned f…
Exponential Concentration Inequalities For Independent Random Vectors Under Sublinear Expectations
本文首次在亚线性期望下提出多变量样本均值的指数集中不等式，通过亚高斯尾界和无维度界等方法，证明了样本均值与Minkowski平均的距离具有最优的亚高斯收敛速率。
We consider the problem of recovering an unknown vector from noisy data with the help of projection estimates. The goal is to find a convex combination of these estimates with the minimal risk. We study an aggregation method based on the so-called exponential weighting and provide a new upper bound for the mean square risk of this method.
The aim of this note is to investigate the concentration properties of unbounded functions of geometrically ergodic Markov chains. We derive concentration properties of centered functions with respect to the square of the Lyapunov's function in the drift condition satisfied by the Markov chain. We apply the new exponential inequalities to derive confidence intervals for MCMC algorithms. Quantitative error bounds are providing for the regenerative Metropolis algorithm of [5].
In this work we introduce a general approach, based on the mar-tingale representation of a sampling design and Azuma-Hoeffding's inequality , to derive exponential inequalities for the difference between a Horvitz-Thompson estimator and its expectation. Applying this idea, we establish such inequalities for Chao's procedure, Till{é}'s elimination procedure, the generalized Midzuno method as well as for Brewer's method. As a by-product, we prove that the first three sampling designs are (conditionally) negatively associated. For such sampling designs, we show that that the inequality we obtain …
In this manuscript we present exponential inequalities for spatial lattice processes which take values in a separable Hilbert space and satisfy certain dependence conditions. We consider two types of dependence: spatial data under $α$-mixing conditions and spatial data which satisfies a weak dependence condition introduced by Dedecker and Prieur [2005]. We demonstrate their usefulness in the functional kernel regression model of Ferraty and Vieu [2004] where we study uniform consistency properties of the estimated regression operator on increasing subsets of the underlying function space.
Exponential inequalities and functional estimations for weak dependent datas ; applications to dynamical systems
我们估计密度和回归函数弱相关数据。使用Dedecker和Prieur以及作者以前的一篇文章中获得的指数不等式，我们控制估计量和函数本身之间的偏差。这些结果适用于一大类动力系统，并导致不变密度和映射本身的估计。
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our development complements recent results by Wei and Dudley (2011) concerning exponential bounds for two-sided Kolmogorov - Smirnov statistics by giving corresponding results for one-sided statistics with emphasis on "adjusted" inequalities of the type proved originally by Dvoretzky, Kiefer, and Wolfowitz (1956) and by Massart (1990) for one-sample versions of thes…
Kolmogorov-Type Maximal Inequalities for Independent and Dependent Negative Binomial Random Variables: Sharp Bounds, Sub-Exponential Refinements, and Applications to Overdispersed Count Data
本文发展了适用于独立和依赖负二项随机变量和的 Kolmogorov 型极大不等式，推导了精确界限和亚指数细化，展示了对超分散计数数据的应用价值。
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