相关论文: Finite-sample Rousseeuw-Croux scale estimators
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
Median-of-means (MOM) based procedures provide non-asymptotic and strong deviation bounds even when data are heavy-tailed and/or corrupted. This work proposes a new general way to bound the excess risk for MOM estimators. The core technique…
Maintaining the quality of manufactured products at a desired level is known to increase customer satisfaction and profitability. Shewhart control chart is the most widely used in statistical process control (SPC) technique to monitor the…
Methods for random-effects meta-analysis require an estimate of the between-study variance, $\tau^2$. The performance of estimators of $\tau^2$ (measured by bias and coverage) affects their usefulness in assessing heterogeneity of…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
We undertake a detailed study of the performance of maximum likelihood (ML) estimators of the density matrix of finite-dimensional quantum systems, in order to interrogate generic properties of frequentist quantum state estimation. Existing…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
The field of discrete event simulation and optimization techniques motivates researchers to adjust classic ranking and selection (R&S) procedures to the settings where the number of populations is large. We use insights from extreme value…
Estimating the mean of a random vector from i.i.d. data has received considerable attention, and the optimal accuracy one may achieve with a given confidence is fairly well understood by now. When the data take values in more general metric…
We study the problem of robust estimation of the mean vector of a sub-Gaussian distribution. We introduce an estimator based on spectral dimension reduction (SDR) and establish a finite sample upper bound on its error that is…
The classical asymptotic theory for parametric $M$-estimators guarantees that, in the limit of infinite sample size, the excess risk has a chi-square type distribution, even in the misspecified case. We demonstrate how self-concordance of…
For differences between means of continuous data from independent groups, the customary scale-free measure of effect is the standardized mean difference (SMD). To justify use of SMD, one should be reasonably confident that the group-level…
Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…
In randomised trials, continuous endpoints are often measured with some degree of error. This study explores the impact of ignoring measurement error, and proposes methods to improve statistical inference in the presence of measurement…
Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees,…
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general…
The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…
We study the algorithmic problem of robust mean estimation of an identity covariance Gaussian in the presence of mean-shift contamination. In this contamination model, we are given a set of points in $\mathbb{R}^d$ generated i.i.d. via the…
There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…