Advances and Applications in Statistics
Volume 38, Issue 1, Pages 37 - 50
(January 2014)
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ASYMPTOTIC EXPANSION OF SAMPLING DISTRIBUTION OF AN MLE TO ACCURACY
Jan Vrbik
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Abstract: We provide formulas for computing and proportional terms of Edgeworth-series expansion of the sampling
distribution of an ML estimator of a single parameter of a given distribution. Furthermore, we show how to transform any such estimator to remove the predominant, proportional term of this expansion. This enables us to find a substantially better approximation to its sampling distribution than that provided by the Central Limit Theorem; we can often use this approximation with a sample size as small as 5. |
Keywords and phrases: maximum likelihood estimator, sampling distribution, Edgeworth series, cumulants, Weibull distribution. |
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