相关论文: Computable exponential bounds for screened estimat…

We investigate the estimation of the extreme value index when the data are subject to random censorship. We prove, in a unified way, detailed asymptotic normality results for various estimators of the extreme value index and use these…

One popular approach to incorporating experimental data into molecular simulations is to restrain the ensemble average of observables to their experimental values. Here I derive equations for the equilibrium distributions generated by…

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…

Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary…

We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical…

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…

The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…

We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress towards an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration…

Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…

Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate…

We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing…

Regression adjustment, sometimes known as Controlled-experiment Using Pre-Experiment Data (CUPED), is an important technique in internet experimentation. It decreases the variance of effect size estimates, often cutting confidence interval…

The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…

Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…

The analysis of a truncated sample can be hindered by censoring. Survival information may be lost to follow-up or the birthdate may be missing. The data can still be modeled as a truncated point process and it is close to a Poisson process,…

The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…

In this article, we derive an explicit formula for computing confidence interval for the mean of a bounded random variable. Moreover, we have developed multistage point estimation methods for estimating the mean value with prescribed…

We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…

For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…

Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…