Bayes, E-Bayes and Robust Bayes Premium Estimation and Prediction under the Squared Log Error Loss Function

BAYES ESTIMATION USING A LINEX LOSS FUNCTION

This paper considers estimation of normal mean ? when the variance is unknown, using the LINEX loss function. The unique Bayes estimate of ? is obtained when the precision parameter has an Inverse Gaussian prior density

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

Robust Bayes

Robust Bayes and Empirical Bayes Analysis with # -Contaminated Priors

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Lower Bounds for Bayes Error Estimation

ÐWe give a short proof of the following result. Let …X; Y † be any distribution on N f0; 1g, and let …X1; Y1†; . . . ; …Xn; Yn† be an i.i.d. sample drawn from this distribution. In discrimination, the Bayes error L ˆ infg Pfg…X† 6ˆ Y g is of crucial importance. Here we show that without further conditions on the distribution of …X; Y †, no rate-of-convergence results can be obtained. Let n…X1; ...

Empirical Bayes and Full Bayes for Signal Estimation

We consider signals that follow a parametric distribution where the parameter values are unknown. To estimate such signals from noisy measurements in scalar channels, we study the empirical performance of an empirical Bayes (EB) approach and a full Bayes (FB) approach. We then apply EB and FB to solve compressed sensing (CS) signal estimation problems by successively denoising a scalar Gaussian...