# The precision of some unbiased regression estimators

##### Williams, W.H.

#### Biometrics 19(2): 352-361

#### 1963

**ISSN/ISBN: 0006-341X**DOI: 10.2307/2527821

Accession: 025890863

In sampling studies one desires unbiased estimators of the mean or total, and that they have good precision. There are many methods of improving precision; the one of interest in this paper is the use of auxiliary information in regression-type estimators. The classical ratio and regression estimators are in general biased, and various forms of exactly unbiased estimators have been proposed. In particular, the present writer Williams, Biometrics, 17, 267-274, has generated unbiased estimators by splitting up the sample in a special way. Different forms of these estimators can be obtained by different selections of arbitrary coefficients. In this paper, the precision of these unbiased estimators is compared with the precision of a least squares procedure in which least squares is known to possess certain optimum properties. Two forms of the unbiased estimators are used; first with the least squares coefficient form and second, with a coefficient in the Wald group average form. The unbiased estimators fare reasonably well provided that the sample is split into a number of groups which is reasonably close to optimum. Multivariate estimators are included in the study.