Finite sample properties of beale's ratio estimator

Abstract

In this paper, the exact blas and mean square error of Beale's ratio estimator are derived under a blvariate normal nlodel in the form of an infinite series. It is found that some conventional large sample approxlmatlons are extremely poor if the relative variance of the auxlllary variable X is large. It is also brought out through this.study that Beale's estimator of the population mean seems to be more efficient than the usual sanple mean under the condition resulting from the large sample comparison of the customary ratio estimator and the usual sample mean.

Keywords:

• ratio estimator
• bias
• mean square error
• bivariate normal distribution