Related papers: Exponential inequalities for sampling designs
A key feature of determinantal sampling designs is their capacity to provide known and parametrisable inclusion probabilities at any order. This paper aims to demonstrate how to effectively leverage this characteristic, highlighting its…
In this article, we present exponential-type inequalities for positive linear mappings and Hilbert space operators, by means of convexity and the Mond-Pe\v cari\'c method. The obtained results refine and generalize some known results. As an…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
In many epidemiological contexts, disease occurrences and their rates are naturally modelled by counting processes and their intensities, allowing an analysis based on martingale methods. These methods lend themselves to extensions of…
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 It\^o's formula and on a new…
It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much…
We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…
Random samples are lossy summaries which allow queries posed over the data to be approximated by applying an appropriate estimator to the sample. The effectiveness of sampling, however, hinges on estimator selection. The choice of…
We systematically investigate issues due to mis-specification that arise in estimating causal effects when (treatment) interference is informed by a network available pre-intervention, i.e., in situations where the outcome of a unit may…
We establish the inferential properties of the mean-difference estimator for the average treatment effect in randomized experiments where each unit in a population is randomized to one of two treatments and then units within treatment…
In this note, we present a version of Hoeffding's inequality in a continuous-time setting, where the data stream comes from a uniformly ergodic diffusion process. Similar to the well-studied case of Hoeffding's inequality for discrete-time…
Randomized experiments are the gold standard for estimating treatment effects, yet network interference challenges the validity of traditional estimators by violating the stable unit treatment value assumption and introducing bias. While…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…
In this paper,we consider a high-dimensional statistical estimation problem in which the the number of parameters is comparable or larger than the sample size. We present a unified analysis of the performance guarantees of exponential…
An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well…
In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…
Survey sampling theory and methods are introduced. Sampling designs and estimation methods are carefully discussed as a textbook for survey sampling. Topics includes Horvitz-Thompson estimation, simple random sampling, stratified sampling,…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
Introduced by Lu and Yau (CMP, 1993), the martingale decomposition method is a powerful recursive strategy that has produced sharp log-Sobolev inequalities for homogeneous particle systems. However, the intractability of certain covariance…