On the ratio and regression estimation in finite population sampling


A simple and more intuitive explanation of the bias of the ratio and the regression estimators of finite population is provided. The finite population is represented by certain regression fits, and the leading term of bias is described in terms of familiar concepts. We show that the asymptotic bias of the ratio estimator is due to intercept of a linear regression fit, whereas for the regression estimator, it is due to the coefficient of the quadratic term of a quadratic regression fit. We also give some variance formulas written in terms of easily interpretable quantities of the linear regression fit. © 1990 American Statistical Association.

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American Statistician