Related papers: An Axiomatisation of Error Intolerant Estimation
In nonparametric statistics, rate-optimal estimators typically balance bias and stochastic error. The recent work on overparametrization raises the question whether rate-optimal estimators exist that do not obey this trade-off. In this work…
Statistical learning theory and the Probably Approximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to analyze learning problems and algorithms, and have been studied thoroughly.…
We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $\sigma^{2}$. Our estimation procedure is based on estimator selection. More precisely, we start with an…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard…
An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected…
This paper presents a new estimator of the intercept of a linear regression model in cases where the outcome varaible is observed subject to a selection rule. The intercept is often in this context of inherent interest; for example, in a…
In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…
Neural point estimators are neural networks that map data to parameter point estimates. They are fast, likelihood free and, due to their amortised nature, amenable to fast bootstrap-based uncertainty quantification. In this paper, we aim to…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…
This paper studies the remote state estimation problem of linear time-invariant systems with stochastic event-triggered sensor schedules in the presence of packet drops between the sensor and the estimator. It is shown that the system state…
Claeskens and Hjort (2003) constructed the focused information criterion (FIC) and developed frequentist model averaging methods using maximum likelihood estimators assuming the observations to be independent and identically distributed.…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…
Devising a fair classifier that does not discriminate against different groups is an important problem in machine learning. Although researchers have proposed various ways of defining group fairness, most of them only focused on the…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
We propose a method to debias estimators based on U-statistics with Machine Learning (ML) first-steps. Standard plug-in estimators often suffer from regularization and model-selection biases, producing invalid inferences. We show that…