Abstract After describing the basic theory of design and modelbased sampling inference and literature review, the controversy between those who accept Royall's modelbased (prediction approach) to inference in finite population sampling and those who continue to use the designbased (randomization) principle even after twenty four years with special reference to Neyman (1934) is discussed. While discussing the controversy, the author has presented his own point of view. A general estimator is introduced. The derivation of this estimator using a strictly designbased approach is given. Empirical and semiempirical studies have been conducted to compare this new strictly designbased estimator with the existing designbased and modelbased estimators. The design and modelbased properties of this general class of estimators have also been discussed. An anticipated variance (Isaki and Fuller, 1982) is derived. It is also proved that the asymptotic form of the estimator under investigation is the Generalized Regression of Cassel, Sarndal and Wretman (1976). The predictive form of this estimator, like Basu (1971), is, presented. An exact and approximate lower bound of the mean square of this general class of estimators is derived and compared with the Godambe Joshi (1965) lower bound of variance. For this purpose, a natural course of action is to limit the class of estimators which are design and modelunbiased. Within this class, we have found the optimum estimator and then derived the lower bound. An approximation to an exact lower bound of mean square error is derived by using Brewer's (1979) concept of asymptotic unbiased ness. A new modelbased variance estimator is derived and compared with the existing designbased and modelbased variance estimators. Some properties of the existing modelbased estimators which remain unexplained so far are also discussed. Finally, a new selection procedure is introduced and using this selection procedure, the Generalized Murthy estimator (or revised ratio estimator) is de rived. The Generalized Murthy estimator is both design and modelunbiased. A small sample performance of this new estimator is studied and it is found to be more stable than the Lahiri's (1951) ratio estimator, and it is as good as those of Horvitz and Thompson (1952) and Murthy (1957).
