Asymptotics of predictive distributions driven by sample means and variances

Abstract
Let be the predictive distributions of a sequence of -variate random variables. Suppose \alpha_n=\mathcal{N}_p(M_n,Q_n) where and . Then, there is a random probability measure on such that weakly a.s. If , one also obtains where is total variation distance. Moreover, the convergence rate of is arbitrarily close to . These results (apart from the one regarding the convergence rate) still apply even if , where belongs to a class of distributions much larger than the normal. Finally, the asymptotic behavior of copula-based predictive distributions (introduced in [13]) is investigated and a numerical experiment is performed.
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