A regression-scale model is of the form y=X\beta+\sigma\epsilon, where X is a fixed nxp design matrix, \beta\in\Real^p an unknown regression coefficient, \sigma>0 a scale parameter, and \epsilon represents an n-dimensional vector of errors whose density is known. Inference is usually made conditionally on the sample configuration a=(y-X\hat\beta)/\hat\sigma, where (\hat\beta,\hat\sigma) are the maximum likelihood estimates. Higher-order asymptotics provide very accurate approximations to exact conditional procedure thus avoiding multidimensional numerical integration. This paper presents how by means of the Metropolis-Hastings algorithm, a powerful Markov Chain Monte Carlo technique, conditional properties of these methods can be assessed. MCMC are necessary, as the conditional distributions involved are only known up to the normalizing constant.
SIMULAZIONI CONDIZIONATE PER FAMIGLIE DI REGRESSIONE E SCALA
BRAZZALE, ALESSANDRA ROSALBA
1998
Abstract
A regression-scale model is of the form y=X\beta+\sigma\epsilon, where X is a fixed nxp design matrix, \beta\in\Real^p an unknown regression coefficient, \sigma>0 a scale parameter, and \epsilon represents an n-dimensional vector of errors whose density is known. Inference is usually made conditionally on the sample configuration a=(y-X\hat\beta)/\hat\sigma, where (\hat\beta,\hat\sigma) are the maximum likelihood estimates. Higher-order asymptotics provide very accurate approximations to exact conditional procedure thus avoiding multidimensional numerical integration. This paper presents how by means of the Metropolis-Hastings algorithm, a powerful Markov Chain Monte Carlo technique, conditional properties of these methods can be assessed. MCMC are necessary, as the conditional distributions involved are only known up to the normalizing constant.
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