Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 3, 289--300

Do Tails Of Symmetric Distributions Contain More Fisher Information About The Scale Parameter

By

G. ZHENG, National Heart Lung and Blood Institute, Bethesda, MD, USA

and

J.L. GASTWIRTH, George Washington University, DC, USA

SUMMARY. Several studies have shown that the tails of an ordered sample from a symmetric distribution contain more Fisher information about the scale parameter than the middle portion. Whether the tails are the most informative symmetric fraction of the ordered data remains of interest. In this note, we provide conditions for two symmetric portions of order statistics to contain the most limiting Fisher information about the scale parameter of Cauchy, Laplace, logistic, and normal distributions. This indicates that highly efficient estimators for the scale parameter of these distributions may be obtained using the order statistics in this most informative region

AMS (1991) subject classification}. 62F07, 62J05, 94A15.

Key words and phrases. Best linear unbiased estimator, censored data, Fisher information, folded distribution, order statistics.

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