Empirical Bayes Estimation with Convergence Rates in Noncontinuous Lebesgue Exponential Families
Empirical Bayes Estimation with Convergence Rates in Noncontinuous Lebesgue Exponential Families
Empirical Bayes estimators, asymptotically optimal with rates, are proposed. In the component problem there is a pair $(X, \omega)$ of real valued random variables. The Lebesgue density of $X$, conditional on $\omega$, is of the form $u(x)C(\omega)e^{\omega x}$. Based on a realization of $X$, the problem is squared error loss …