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The possibility of improving on the usual multivariate normal confidence was first discussed in Stein (1962). Using the ideas of shrinkage, through Bayesian and empirical Bayesian arguments, domination results, both analytic and numerical, have been obtained. Here we trace some of the developments in confidence set estimation.
The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level often happ
We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both
A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough simulation
Introductory texts on statistics typically only cover the classical two sigma confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this gap by first
We consider the problem of simultaneous estimation of a sequence of dependent parameters that are generated from a hidden Markov model. Based on observing a noise contaminated vector of observations from such a sequence model, we consider simultaneou