Asymptotic loss of the MLE of a truncation parameter in the presence of a nuisance parameter for a one-sided truncated family of distributions

Abstract

For a truncated family of distributions with a truncation parameter γ and a parameter θ as a nuisance parameter, we derive the stochastic expansions of bias-adjusted maximum likelihood estimators and of γ based on a sample of size n when θ is known and when θ is unknown, respectively. The asymptotic loss of relative to is obtained up to the second order, that is the order n −1. The results are a generalization of those for a one-sided truncated exponential family of distributions. Its application to truncated t-distributions is also given.