Sample Survey Theory Some Pythagorean Perspectives

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. Step by step, 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 whole family of different sampling designs, varying from simple surveys to complex surveys based on multistage sampling without replacement and unequal probabilities. This volume will be useful for survey practitioners faced with complex surveys. The book also considers constrained estimation problems that may occur in practice when linear or nonlinear economic restrictions are imposed on the population parameters to be estimated and the observations stem from different surveys. For example, regression estimators and consistent estimation of contingency tables are special cases within this rather broad class of constrained estimators. This volume also offers a guide to little-known connections between design-based survey sampling and other areas of statistics and related disciplines. The common underlying principles in the distinct fields are explained by an extensive use of the geometry of the ancient Pythagorean theorem. Apart from its applied importance, the book may also serve as a textbook in advanced courses and as a reference for researchers in statistics and empirical economics. In order to make the text as self-contained as possible, the treatise includes one chapter with the main results from statistics, including regression analysis. Some familiarity with calculus and matrix algebra is a sufficient prerequisite. Paul Knottnerus received his PhD in economics in 1989 from the University of Amsterdam. In 1995 he joined Statistics Netherlands, Department of Methods and Informatics. Previously he spent several years with Dutch Telecom. He is author of the book Linear Models with Correlated Disturbances (1991).