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

HaiYing Wang and Nancy Flournoy

Statistics & Probability Letters, 2015, vol. 105, issue C, 57-64

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.

Keywords: Consistency; Local maximum; Maximum likelihood; Non-regular model; Uniform local asymptotic normality (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.05.021

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