Asymptotic Normality of Posterior Distributions for Exponential Families with Many Parameters
نویسنده
چکیده
We study consistency and asymptotic normality of posterior distributions of the natural parameter for an exponential family when the dimension of the parameter grows with the sample size. Under certain growth restrictions on the dimension, we show that the posterior distributions concentrate in neighbourhoods of the true parameter and can be approximated by an appropriate normal distribution.
منابع مشابه
Asymptotic Normality of Posterior Distributions for Exponential Families when the Number of Parameters Tends to Infinity
Exponential families arise naturally in statistical modelling and the maximum likelihood estimate (MLE) is consistent and asymptotically normal for these models [Berk [2]]. In practice, often one needs to consider models with a large number of parameters, particularly if the sample size is large; see Huber [14], Haberman [13] and Portnoy [18 21]. One may also think that the true model can only ...
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تاریخ انتشار 1996