Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series B, Pt. 2, pp. 184--198

BEST LINEAR UNBIASED ESTIMATION OF THE POPULATION MEAN UNDER SEQUENTIAL SAMPLING

By

B. K. GHOSH, Lehigh University

and

N. J. SCHMITZ, University of Münster

SUMMARY.  A systematic study is undertaken on the best linear unbiased estimation (BLUE) of the population mean under sequential sampling procedures. When the stopping rule is random but does not depend on the observations, the BLUE is obtained explicitly and it is shown that the simple mean, though not a BLUE, has an optimum property. Whe the stopping rule depends on the observations in a Markovian way, a global BLUE may not exist or may exist but is inefficient depending on the nature of the stopping rule. In particular, the sample mean is shown to be biased for the exponential family of distributions under certain well-known stopping rules.

AMS (1980) subject classification.  62L12, 62F10, 62G05.

Key words and phrases. Sequential estimation, BLUE in the sequential case, sample mean as an estimator, exponential families.

Full paper (PDF)

This article in Mathematical Reviews.