Limiting Properties of Empirical Bayes Estimators in a Two-Factor Experiment under Inverse Gaussian Model

Abstract

The empirical Bayes estimators of treatment effects in a factorial experiment were derived and their asymptotic properties were explored. It was shown that they were asymptotically optimal and the estimator of the scale parameter had a limiting gamma distribution while the estimators of the factor effects had a limiting multivariate normal distribution. A Bootstrap analysis was performed to illustrate the theoretical results empirically.