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

M. Akahira and N. Ohyauchi

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 12, 6085-6097

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 γ^ML*θ$\hat{\gamma }_{ML^*}^\theta$ and γ^ML*$\hat{\gamma }_{ML^*}$ of γ when θ is known and when θ is unknown, respectively, are derived. The second-order asymptotic loss of γ^ML*$\hat{\gamma }_{ML^*}$ relative to γ^ML*θ$\hat{\gamma }_{ML^*}^\theta$ is also obtained through their asymptotic variances. Further, some examples are given.

Date: 2017
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DOI: 10.1080/03610926.2015.1117638

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