Maximum Likelihood Estimation for a One-Sided Truncated Family of Distributions

Masafumi Akahira ()
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Masafumi Akahira: Uninversity of Tsukuba, Professor Emeritus

Chapter Chapter 6 in Theory of Statistical Estimation, 2026, pp 145-174 from Springer

Abstract: Abstract For a one-sided truncated family of distributions with an interest parameter θ $$\theta $$ and a truncation parameter γ $$\gamma $$ as a nuisance parameter, we consider the maximum likelihood estimators (MLEs) θ ̂ ML γ $$\hat \theta _{ML}^\gamma $$ and θ ̂ ML $$\hat \theta _{ML}$$ of θ $$\theta $$ for known γ $$\gamma $$ and unknown γ $$\gamma $$ , respectively. In this chapter, the stochastic expansions of θ ̂ ML γ $$\hat \theta _{ML}^\gamma $$ and θ ̂ ML $$\hat \theta _{ML}$$ are derived, and their second order asymptotic variances are obtained. The second order asymptotic loss of a bias-adjusted MLE θ ̂ M L ∗ $$\hat \theta _{ML^*}$$ relative to θ ̂ ML γ $$\hat \theta _{ML}^\gamma $$ is also given. The results are a generalization of those for a one-sided truncated exponential family of distributions. Examples on a one-sided truncated Cauchy distribution, a general truncated exponential family, etc. are also given.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-95-5339-6_6

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DOI: 10.1007/978-981-95-5339-6_6

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