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In this paper, we consider the estimation of a mean vector of a multivariate normal population where the mean vector is suspected to be nearly equal to mean vectors of $k-1$ other populations. As an alternative to the preliminary test…

Statistics Theory · Mathematics 2018-09-10 Ryo Imai , Tatsuya Kubokawa , Malay Ghosh

We consider the problem of statistical inference on parameters of a target population when auxiliary observations are available from related populations. We propose a flexible empirical Bayes approach that can be applied on top of any…

Statistics Theory · Mathematics 2023-12-15 Michael Law , Peter Bühlmann , Ya'acov Ritov

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…

Numerical Analysis · Mathematics 2021-03-30 Jiahui Zhang , Anne Gelb , Theresa Scarnati

Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…

Methodology · Statistics 2021-03-02 Spencer Woody , Oscar Hernan Madrid Padilla , James G. Scott

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Statistics Theory · Mathematics 2024-02-26 Dapeng Yao , Fangzheng Xie , Yanxun Xu

In this article, we investigate certain asymptotic optimality properties of a very broad class of one-group continuous shrinkage priors for simultaneous estimation and testing of a sparse normal mean vector. Asymptotic optimality of Bayes…

Statistics Theory · Mathematics 2015-11-11 Prasenjit Ghosh , Arijit Chakrabarti

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…

Statistics Theory · Mathematics 2007-06-13 Iain M. Johnstone , Bernard W. Silverman

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…

Methodology · Statistics 2017-02-28 Shonosuke Sugasawa , Tatsuya Kubokawa

The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach, that treats the…

Methodology · Statistics 2017-01-04 Asaf Weinstein , Zhuang Ma , Lawrence D. Brown , Cun-Hui Zhang

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…

Methodology · Statistics 2017-11-29 Wentao Li , Paul Fearnhead

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…

Statistics Theory · Mathematics 2013-11-21 Kengo Kato

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

Statistics Theory · Mathematics 2009-09-29 Subhashis Ghosal , Aad van der Vaart

Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator of the population mean. For variance estimation,…

Methodology · Statistics 2018-01-16 Shu Yang , Jae Kwang Kim

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

Statistics Theory · Mathematics 2026-03-31 Taehyun Kim , Bodhisattva Sen

We study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…

Statistics Theory · Mathematics 2017-08-01 Gourab Mukherjee , Iain M. Johnstone

Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however,…

Statistics Theory · Mathematics 2020-10-15 Jeffrey P. Spence

Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…

Statistics Theory · Mathematics 2025-08-04 Chang Liu , Ryan Martin , Weining Shen

We consider the asymptotic behaviour of the marginal maximum likelihood empirical Bayes posterior distribution in general setting. First we characterize the set where the maximum marginal likelihood estimator is located with high…

Statistics Theory · Mathematics 2016-04-05 Judith Rousseau , Botond Szabo

We consider the classical problem of estimating a vector $\bolds{\mu}=(\mu_1,...,\mu_n)$ based on independent observations $Y_i\sim N(\mu_i,1)$, $i=1,...,n$. Suppose $\mu_i$, $i=1,...,n$ are independent realizations from a completely…

Statistics Theory · Mathematics 2009-08-13 Lawrence D. Brown , Eitan Greenshtein