相关论文: High confidence estimates of the mean of heavy-tai…
The median absolute deviation (MAD) is a robust measure of scale that is simple to implement and easy to interpret. Motivated by this, we introduce interval estimators of the MAD to make reliable inferences for dispersion for a single…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
A powerful robust mean estimator introduced by Catoni (2012) allows for mean estimation of heavy-tailed data while achieving the performance characteristics of classical mean estimator for sub-Gaussian data. While Catoni's framework has…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…
Estimating average treatment effects from observational data is challenging under practical violations of the positivity assumption. Targeted Maximum Likelihood Estimators (TMLEs) are widely used because of their double robustness and…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable,…
Input variables in numerical models are often subject to several levels of uncertainty, usually modeled by probability distributions. In the context of uncertainty quantification applied to these models, studying the robustness of output…
Average calibration of the (variance-based) prediction uncertainties of machine learning regression tasks can be tested in two ways: one is to estimate the calibration error (CE) as the difference between the mean absolute error (MSE) and…
This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…
The article starts with new aliasing-truncation error upper bounds in the sampling theorem for non-bandlimited stochastic signals. Then, it investigates $L_p([0,T])$ approximations of sub-Gaussian random signals. Explicit truncation error…
We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…
We study mean change point testing problems for high-dimensional data, with exponentially- or polynomially-decaying tails. In each case, depending on the $\ell_0$-norm of the mean change vector, we separately consider dense and sparse…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…
Recent variational inference methods use stochastic gradient estimators whose variance is not well understood. Theoretical guarantees for these estimators are important to understand when these methods will or will not work. This paper…
In this work, we analyze the variance of a stochastic estimator for computing Schatten norms of matrices. The estimator extracts information from a single sketch of the matrix, that is, the product of the matrix with a few standard Gaussian…
We study operator-norm covariance estimation from heavy-tailed samples that may include a small fraction of arbitrary outliers. A simple and widely used safeguard is \emph{Euclidean norm clipping}, but its accuracy depends critically on an…
Compositional data, which is data consisting of fractions or probabilities, is common in many fields including ecology, economics, physical science and political science. If these data would otherwise be normally distributed, their spread…