Related papers: Bayesian Shrinkage Estimation for Stratified Count…
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors…
We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…
Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…
In this note, we consider the problem of estimating multinomial cell probabilities under the entropy loss when side information in aggregated data is available. We use the Jeffreys prior to obtain Bayes estimators. It is shown that by…
Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at…
In this article, we consider two forms of shrinkage estimators of the mean $\theta$ of a multivariate normal distribution $X\sim N_{p}\left(\theta, \sigma^{2}I_{p}\right)$ where $\sigma^{2}$ is unknown. We take the prior law $\theta \sim…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
The exponential distribution is applied in a very wide variety of statistical procedures. Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for…
This paper addresses the weak instruments problem in linear instrumental variable models from a Bayesian perspective. The new approach has two components. First, a novel predictor-dependent shrinkage prior is developed for the many…
We develop and analyze empirical Bayes Stein-type estimators for use in the estimation of causal effects in large-scale online experiments. While online experiments are generally thought to be distinguished by their large sample size, we…
Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
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,…
This paper presents a simple shrinkage estimator of rates based on Bayesian methods. Our focus is on crime rates as a motivating example. The estimator shrinks each town's observed crime rate toward the country-wide average crime rate…
We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or…
A doubly type-II censored scheme is an important sampling scheme in the life testing experiment and reliability engineering. In the present commutation, we have considered estimating ordered scale parameters of two exponential distributions…
In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…