Related papers: A Note on Improved Multivariate Normal Mean Estima…
In observational causal inference, domain knowledge often leaves multiple covariate adjustments plausible, yet which sets satisfy ignorability is untestable. Different adjustment sets can yield conflicting estimates of the average treatment…
We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…
We study average treatment effect (ATE) estimation under complete randomization with many covariates in a design-based, finite-population framework. In randomized experiments, regression adjustment can improve precision of estimators using…
In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi (1969). This solves a long-standing open problem…
A major problem in numerical weather prediction (NWP) is the estimation of high-dimensional covariance matrices from a small number of samples. Maximum likelihood estimators cannot provide reliable estimates when the overall dimension is…
In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum…
We study the problem of estimating the mean of a random vector in $\mathbb{R}^d$ based on an i.i.d.\ sample, when the accuracy of the estimator is measured by a general norm on $\mathbb{R}^d$. We construct an estimator (that depends on the…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…
Under a multinormal distribution with arbitrary unknown covariance matrix, the main purpose of this paper is to propose a framework to achieve the goal of reconciliation of Bayesian, frequentist and Fisherian paradigms for the problems of…
Random-effects meta-analyses are very commonly used in medical statistics. Recent methodological developments include multivariate (multiple outcomes) and network (multiple treatments) meta-analysis. Here we provide a new model and…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…
Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…
In a regression model with multiple response variables and multiple explanatory variables, if the difference of the mean vectors of the response variables for different values of explanatory variables is always in the direction of the first…
Within the last few years, there has been a move towards using statistical models in conjunction with neural networks with the end goal of being able to better answer the question, "what do our models know?". From this trend, classical…
This paper investigates when the importance weighting (IW) correction is needed to address covariate shift, a common situation in supervised learning where the input distributions of training and test data differ. Classic results show that…
Large language models (LLMs) have been proposed as alternatives to human experts for estimating unknown quantities with associated uncertainty, a process known as Bayesian elicitation. We test this by asking eleven LLMs to estimate…
We consider the $p$-generalized arithmetic-geometric mean inequality for vectors chosen randomly from the $\ell_p^n$-ball in $\mathbb{R}^n$. In this setting the inequality can be improved or reversed up to a respective scalar constant with…
We study regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We provide a detailed proof of asymptotic normality of the covariate-adjusted estimator under minimal…
For a given $p$-variable mean $M \colon I^p \to I$ ($I$ is a subinterval of $\mathbb{R}$), following (Horwitz, 2002) and (Lawson and Lim, 2008), we can define (under certain assumption) its $(p+1)$-variable $\beta$-invariant extension as…