Related papers: Minimaxity under the half-Cauchy prior

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes…

We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a…

We study the problem of loss estimation that involves for an observable $X \sim f_{\theta}$ the choice of a first-stage estimator $\hat{\gamma}$ of $\gamma(\theta)$, incurred loss $L=L(\theta, \hat{\gamma})$, and the choice of a…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

We introduce Bayesimax theory, a paradigm for objective Bayesian analysis which selects priors by applying minimax theory to prior disclosure games. In these games, the uniquely optimal strategy for a Bayesian agent upon observing the data…

This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…

In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very…

Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional…

Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical…

Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…

This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional…

We consider high-dimensional multivariate linear regression models, where the joint distribution of covariates and response variables is a multivariate normal distribution with a bandable covariance matrix. The main goal of this paper is to…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

In this work, we delve into the nonparametric empirical Bayes theory and approximate the classical Bayes estimator by a truncation of the generalized Laguerre series and then estimate its coefficients by minimizing the prior risk of the…

In this paper, we consider simultaneous estimation of Poisson parameters in situations where we can use side information in aggregated data. We use standardized squared error and entropy loss functions. Bayesian shrinkage estimators are…

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…