The weighted residual technique for estimating the variance of the general regression estimator of the finite population total

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.