Extended linear empirical Bayes estimation
empirical Bayes; linear approximation; MODELS; Statistics & Probability
In this paper, the linear empirical Bayes estimation method, which is based on approximation of the Bayes estimator by a linear function, is generalized to an extended linear empirical Bayes estimation technique which represents the Bayes estimator by a series of algebraic polynomials. The extended linear empirical Bayes estimators are elaborated in the case of a location or a scale parameter. The theory is illustrated by examples of its application to the normal distribution with a location parameter and the gamma distribution with a scale parameter. The linear and the extended linear empirical Bayes estimators are constructed in these two cases and, then, studied numerically via Monte Carlo simulations. The simulations show that the extended linear empirical Bayes estimators have better convergence rates than the traditional linear empirical Bayes estimators.
Communications in Statistics-Theory and Methods
Pensky, M., Ni, P. (2000). Extended linear empirical Bayes estimation. Communications in Statistics-Theory and Methods, 29(3). doi: 10.1080/03610920008832503