Likelihood Inference for Linear Regression Models

Approximate conditional inference based on large-sample likelihood ratio methods is considered for the parameters of linear regression models. Mean and variance adjustments that improve the standard normal approximation to the conditional distribution of the signed square root of the log likelihood ratio statistic for a scalar parameter of interest are given. A Bartlett adjustment factor that improves the chi-squared approximation to the conditional distribution of the log likelihood ratio statistic for a vector parameter of interest is also presented. The accuracy of approximate confidence limits obtained by using the adjustments is demonstrated for a location-scale analysis of Darwins data.