ON THE RANKED-SET SAMPLING M-ESTIMATES FOR SYMMETRIC LOCATION FAMILIES

XIAOYUE ZHAO^{1} AND ZEHUA CHEN^{2}

1Department of Statistics, University of California, 367 Evans Hall, Berkeley, CA 94720-3860, U.S.A.

2Department of Statistics & Applied Probability, National University of Singapore, 3 Science Drive 2, Singapore 117543, Republic of Singapore, e-mail: stachenz@nus.edu.sg

(Received April 6, 2000; revised June 11, 2001)

Abstract. The ranked-set sampling (RSS) is applicable in practical problems where the variable of interest for an observed item is costly or time-consuming but the ranking of a set of items according to the variable can be easily done without actual measurement. In this article, the M-estimates of location parameters using RSS data are studied. We deal mainly with symmetric location families. The asymptotic properties of M-estimates based on ranked-set samples are established. The properties of unbalanced ranked-set sample M-estimates are employed to develop the methodology for determining optimal ranked-set sampling schemes. The asymptotic relative efficiencies of ranked-set sample M-estimates are investigated. Some simulation studies are reported.

Key words and phrases: Asymptotic normality, asymptotic relative efficiency, Mestimates, optimal sampling design, ranked-set sampling, robustness.