Laplace approximations for censored linear regression models |
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Authors: | George D Papandonatos Seymour Geisser |
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Abstract: | We consider approximate Bayesian inference about scalar parameters of linear regression models with possible censoring. A second-order expansion of their Laplace posterior is seen to have a simple and intuitive form for logconcave error densities with nondecreasing hazard functions. The accuracy of the approximations is assessed for normal and Gumbel errors when the number of regressors increases with sample size. Perturbations of the prior and the likelihood are seen to be easily accommodated within our framework. Links with the work of DiCiccio et al. (1990) and Viveros and Sprott (1987) extend the applicability of our results to conditional frequentist inference based on likelihood-ratio statistics. |
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Keywords: | Bayesian inference likelihood inference linear regression censored data Laplace approximation second-order asymptotics |
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