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On the consistency of the maximum likelihood estimator for the three parameter lognormal distribution

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  • Wang, HaiYing
  • Flournoy, Nancy

Abstract

The three parameter log-normal distribution is a popular non-regular model, but surprisingly, whether the local maximum likelihood estimator (MLE) for parameter estimation is consistent or not has been speculated about since the 1960s. This note gives a rigorous proof for the existence of a consistent MLE for the three parameter log-normal distribution, which solves a problem that has been recognized and unsolved for 50 years. Our results also imply a uniform local asymptotic normality condition for the three parameter log-normal distribution. In addition, we give results on the asymptotic normality and the uniqueness of the local MLE.

Suggested Citation

  • Wang, HaiYing & Flournoy, Nancy, 2015. "On the consistency of the maximum likelihood estimator for the three parameter lognormal distribution," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 57-64.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:57-64
    DOI: 10.1016/j.spl.2015.05.021
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    References listed on IDEAS

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    1. Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729, November.
    2. Basak, Prasanta & Basak, Indrani & Balakrishnan, N., 2009. "Estimation for the three-parameter lognormal distribution based on progressively censored data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3580-3592, August.
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