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- W4200562800 abstract "Let S be a Borel subset of a Polish space and F the set of bounded Borel functions f:S→R. Let an(·)=P(Xn+1∈·∣X1,…,Xn) be the n-th predictive distribution corresponding to a sequence (Xn) of S-valued random variables. If (Xn) is conditionally identically distributed, there is a random probability measure μ on S such that ∫fdan⟶a.s.∫fdμ for all f∈F. Define Dn(f)=dn∫fdan−∫fdμ for all f∈F, where dn>0 is a constant. In this note, it is shown that, under some conditions on (Xn) and with a suitable choice of dn, the finite dimensional distributions of the process Dn=Dn(f):f∈F stably converge to a Gaussian kernel with a known covariance structure. In addition, Eφ(Dn(f))∣X1,…,Xn converges in probability for all f∈F and φ∈Cb(R)." @default.
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- W4200562800 date "2021-12-12" @default.
- W4200562800 modified "2023-10-16" @default.
- W4200562800 title "A Central Limit Theorem for Predictive Distributions" @default.
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