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Biometrika 1989 76(3):527-537; doi:10.1093/biomet/76.3.527
© 1989 by Biometrika Trust
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The weighted residual technique for estimating the variance of the general regression estimator of the finite population total

CARL-ERIK SÄRNDAL, BENGT SWENSSON and JAN H. WRETMAN

Départment de mathématiques et de statistique, Universiteé de Montréal Montréal, Queébec H3C 3J7, Canada
Institutionen för dataanalys Högskolan i Örebro, S-701 30 Örebro, Sweden
U/STM, Statistics Sweden S-115 81 Stockholm, Sweden

The paper deals with design based estimation of the variance of the general regression estimator of the finite population total. The usual Taylor linearization variance estimator is an expression in the design weighted regression residuals; in many applications the resulting expression is counterintuitive from a model based standpoint. The improved variance estimator in this paper attaches another simple weight, called ‘g-weight’, to each individual residual. This new variance estimator(i) gives valid design-based confidence intervals, (ii) is nearly unbiased under a suitably chosen regression model, and (iii) works well for conditional inference. Examples are given.

Key Words: Conditional inference • Confidence interval • Design-based inference • Regression estimator • Survey sampling • Variance estimation


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