ESTIMATION OF THE COMMON MEAN OF A BIVARIATE NORMAL POPULATION

PHILIP L. H. YU^{1}, YIJUN SUN^{2} AND BIMAL K. SINHA^{2}

1Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road,

Hong Kong, CHINA

2Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21228-5398, U.S.A.

(Received December 14, 2000; revised June 1, 2001)

Abstract. In this paper we discuss the problem of estimating the common mean of a bivariate normal population based on paired data as well as data on one of the marginals. Two double sampling schemes with the second stage sampling being either a simple random sampling (SRS) or a ranked set sampling (RSS) are considered. Two common mean estimators are proposed. It is found that under normality, the proposed RSS common mean estimator is always superior to the proposed SRS common mean estimator and other existing estimators such as the RSS regression estimator proposed by Yu and Lam (1997, Biometrics, 53, 1070–1080). The problem of estimating the mean Reid Vapor Pressure (RVP) of regular gasoline based on field and laboratory data is considered.

Key words and phrases: Ranked set sampling, relative precision, REML, simple random sampling.