Estimation of Finite Population Variance, Regression Coefficient

Abstract

In this chapter we consider estimation of a finite population variance and regression coefficient. The estimation of population variance is of considerable importance in many circumstances. The geneticsts often classify their population according to population variance [Thompson and Thoday (1979)]. In allocating sample size in a stratified random sampling according to optimum allocation rules, the stratum standard deviations are required to be estimated. Sections 5.2 through 5.4 consider design-based, model-based and Bayes prediction of a finite population variance. Section 5.5 considers some asymptotic properties of a sample regression coefficient. The next section considers pm-unbiased prediction of the slope parameter in the linear regression model. The concluding section addresses optimal prediction of the finite population regression coefficient under multiple regression model.