Related papers: Robust Empirical Bayes Small Area Estimation with …
We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference…
The empirical Bayes estimators in mixed models are useful for small area estimation in the sense of increasing precision of prediction for small area means, and one wants to know the prediction errors of the empirical Bayes estimators based…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
A single primary sampling unit (PSU) per stratum design is a popular design for estimating the parameter of interest. Although, the point estimator of the design is unbiased and efficient, an unbiased variance estimator does not exist. A…
In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…
We develop constrained Bayesian estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates; and benchmarking constraints,…
Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…
In this paper a method of obtaining smooth analytical estimates of probability densities, radial distribution functions and potentials of mean force from sampled data in a statistically controlled fashion is presented. The approach is…
Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…
We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…
Outliers can seriously distort statistical inference by inducing excessive sensitivity in the likelihood function, thereby compromising the reliability of Bayesian estimation. To address this issue, we develop a robust Bayesian estimation…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
Empirical Bayes is a versatile approach to `learn from a lot' in two ways: first, from a large number of variables and second, from a potentially large amount of prior information, e.g. stored in public repositories. We review applications…
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…
Bayes factors for composite hypotheses have difficulty in encoding vague prior knowledge, as improper priors cannot be used and objective priors may be subjectively unreasonable. To address these issues I revisit the posterior Bayes factor,…