Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 2, 178--192

THE OPTIMAL RANKED-SET SAMPLING SCHEME FOR PARAMETRIC FAMILIES

By

ZEHUA CHEN,

and

ZHIDONG BAI, National University of Singapore

SUMMARY. The original balanced ranked-set sampling first proposed by McIntyre (1952) is more efficient than the simple random sampling when the measurement of an observed item is costly and/or time consuming but the ranking of a set of items can be easily done without actual measurement. The efficiency of the original ranked-set sampling can be further improved by unbalanced ranked-set sampling when the knowledge of the underlying distribution is available. In this article, we propose a methodology for determining optimal unbalanced ranked-set sampling scheme in the sense of asymptotic D-optimality or A-optimality. We deal mainly with location-scale families. The methodology is illustrated by applications to two important examples of location-scale families: the normal distributions and the extreme value distributions.

AMS (1991) subject classification. Primary 62F07, 62D05; secondary 62K05, 62G30.

Key words and phrases. Ranked-set sampling; optimal sampling design; D-optimality; A-optimality; maximum likelihood estimate; best linear unbiased estimate.

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