Related papers: Jackknife variance estimation for common mean esti…
A basic result is that the sample variance for i.i.d. observations is an unbiased estimator of the variance of the underlying distribution (see for instance Casella and Berger (2002)). But what happens if the observations are neither…
The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class…
The simplest and most widely applied method for guaranteeing differential privacy is to add instance-independent noise to a statistic of interest that is scaled to its global sensitivity. However, global sensitivity is a worst-case notion…
We consider the problem of combining data from observational and experimental sources to make causal conclusions. This problem is increasingly relevant, as the modern era has yielded passive collection of massive observational datasets in…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
For small area estimation of area-level data, the Fay-Herriot model is extensively used as a model based method. In the Fay-Herriot model, it is conventionally assumed that the sampling variances are known whereas estimators of sampling…
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…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…
A common problem in analysis of experiments or in lattice QCD simulations is fitting a parameterized model to the average over a number of samples of correlated data values. If the number of samples is not infinite, estimates of the…
Standard practice obtains an unbiased variance estimator by dividing by $N-1$ rather than $N$. Yet if only half the data are used to compute the mean, dividing by $N$ can still yield an unbiased estimator. We show that an alternative mean…
We propose confidence sequences -- sequences of confidence intervals which are valid uniformly over time -- for quantiles of any distribution over a complete, fully-ordered set, based on a stream of i.i.d. observations. We give methods both…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
The infinitesimal jackknife (IJ) has recently been applied to the random forest to estimate its prediction variance. These theorems were verified under a traditional random forest framework which uses classification and regression trees…
This review traces the evolution of theory that started when Charles Stein in 1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206, Univ. California Press] showed that using each separate sample mean from $k\ge3$…
We present a second-order estimator of the mean of a variable subject to missingness, under the missing at random assumption. The estimator improves upon existing methods by using an approximate second-order expansion of the parameter…
Clinical prediction models are estimated using a sample of limited size from the target population, leading to uncertainty in predictions, even when the model is correctly specified. Generally, not all patient profiles are observed…
Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…
A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…
Double blind randomized controlled trials are traditionally seen as the gold standard for causal inferences as the difference-in-means estimator is an unbiased estimator of the average treatment effect in the experiment. The fact that this…
A Lorenz curve is a graphical representation of the distribution of income or wealth within a population. The generalized Lorenz curve can be created by scaling the values on the vertical axis of a Lorenz curve by the average output of the…