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

M. Akahira and N. Ohyauchi

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 21, 7526-7540

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 γ̂ML∗θ and γ̂ML∗ of γ based on a sample of size n when θ is known and when θ is unknown, respectively. The asymptotic loss of γ̂ML∗ relative to γ̂ML∗θ 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.

Date: 2024
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DOI: 10.1080/03610926.2023.2269436

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