Strong Consistency of Bayes Estimates in Stochastic Regression Models

摘要

Under minimum assumptions on the stochastic regressors, strong consistency of Bayes estimates is established in stochastic regression models in two cases: (1) When the prior distribution is discrete, the p.d.f.fof i.i.d. random errors is assumed to have finite Fisher information I=∫_(-∞)~∞(f')2/f dx<∞; (2) for general priors, we assumefis strongly unimodal. The result can be considered as an application of a theorem of Doob to stochastic regression models.