TITLE:
Non-Regular Example of Confidence-Interval Construction
AUTHORS:
Jan Vrbik
KEYWORDS:
Non-Regular Parameter Estimation, Maximum-Likelihood Estimator, Asymptotic Distribution, Largest-Order Statistic, Monte-Carlo Simulation
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.4,
August
9,
2023
ABSTRACT: When
dealing with a regular (fixed-support) one-parameter distribution, the
corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally
distributed. But, when the support boundaries are functions of the parameter,
finding good approximation for the sampling distribution of MLE (needed to
construct an accurate confidence interval for the parameter’s true value) may
get very challenging. We demonstrate the nature of this problem, and show how
to deal with it, by a detailed study of a specific situation. We also indicate
several possible ways to bypass MLE by proposing alternate estimators; these,
having relatively simple sampling distributions, then make constructing a confidence
interval rather routine.