We study consistency and asymptotic normality of posterior distributions of the regression coefficient in a linear model when the dimension of the parameter grows with increasing sample size. Under certain growth restrictions on the dimension (depending on the design matrix), we show that the posterior distributions concentrate in neighbourhoods of the true parameter and can be approximated by an appropriate normal distribution.
Publié le : 1999-04-14
Classification:
high dimension,
linear model,
normal approximation,
posterior consistency,
posterior distribution
@article{1173147909,
author = {Ghosal, Subhashis},
title = {Asymptotic normality of posterior distributions in high-dimensional linear models},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 315-331},
language = {en},
url = {http://dml.mathdoc.fr/item/1173147909}
}
Ghosal, Subhashis. Asymptotic normality of posterior distributions in high-dimensional linear models. Bernoulli, Tome 5 (1999) no. 6, pp. 315-331. http://gdmltest.u-ga.fr/item/1173147909/