Estimating regression coefficients from survey data by asymptotic design-cum-model based approach

Postulating a linear regression of a variable of interest on an auxiliary variable with values of the latter known for all units of a survey population, the authors consider appropriate ways of choosing a sample and estimating the regression parameters. Recalling Thomsen’s results on non-existence of ‘design-cum-model’ based minimum variance unbiased estimators of regression coefficients we apply Brewer’s ‘asymptotic’ analysis to derive ‘asymptotic-design-cum-model’ based optimal estimators assuming large population and sample sizes. A variance estimation procedure is also proposed.