Sampling properties of the Bayesian posterior mean with an application to WALS estimation

Many statistical and econometric learning methods rely on Bayesian ideas. When applied in a frequentist setting, their precision is often assessed using the posterior variance. This permissible asymptotically, but not necessarily finite samples. We explore this issue focusing weighted-average least squares (WALS), Bayesian-frequentist ‘fusion’. Exploiting sampling properties of mean normal location model, we derive estimators finite-sample bias variance WALS. study performance proposed an empirical application closely related Monte Carlo experiment which analyze impact legalized abortion crime.