Second-order asymptotic loss of the MLE of a truncation parameter for a truncated exponential family of distributions

ABSTRACT

For a truncated exponential family of distributions with a truncation parameter γ and a natural parameter θ as a nuisance parameter, the stochastic expansions of bias-adjusted maximum likelihood estimators and of γ when θ is known and when θ is unknown, respectively, are derived. The second-order asymptotic loss of relative to is also obtained through their asymptotic variances. Further, some examples are given.