Sample Survey Theory: Some Pythagorean Perspectives

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This book describes a novel approach to the theory of sampling from finite populations. The new unifying approach is based on the sampling autocorrelation coefficient. The author derives a general set of sampling equations that describe the estimators, their variances as well as the corresponding variance estimators. These equations are applicable for a family of different sampling designs, varying from simple surveys to complex surveys based on multistage sampling without replacement and unequal probabilities. The book also considers constrained estimation problems that may occur when linear or nonlinear economic restrictions are imposed on the population parameters to be estimated and the observations stem from different surveys. This volume also offers a guide to little-known connections between design-based survey sampling and other areas of statistics. The common underlying principles in the distinct fields are explained by an extensive use of the geometry of the ancient Pythagorean theorem.