LARGE DEVIATION APPROXIMATIONS FOR MAXIMUM LIKELIHOOD
ESTIMATORS
Abstract: A large deviation expansion of the density of a maximum likelihood estimator is
derived in the case of replications from a multivariate curved subfamily of a continuous
exponential family. Apart from an exponentially decreasing term, the approximation
deviates only by a relative error of order from the true density in a fixed
neighbourhood of the true parameter value. An example is given which shows an
excellent tail approximation even for small The results are specialized to the
multidimensional nonlinear normal regression models and it is shown that, in these models,
the approximation may be improved to deviate only by an exponentially decreasing error
term.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -