Focusing on the classical statistical questions of estimating population means from sample data, this volume presents a compilation of two discussion papers and supplementary notes from a course at Statistics Netherlands. The first paper introduces a new method for addressing unequal probability sampling, while the second explores constrained estimators within specified parameter restrictions. The work systematically examines sampling theory through the lens of the sampling autocorrelation coefficient, a concept integral to both sampling and time series analysis, highlighting its broader implications.
This book presents a novel approach to sampling theory from finite populations, centered around the sampling autocorrelation coefficient. The author systematically derives a comprehensive set of sampling equations that detail estimators, their variances, and corresponding variance estimators, applicable across a range of sampling designs from simple to complex multistage sampling without replacement and unequal probabilities. It serves as a valuable resource for survey practitioners dealing with intricate surveys. Additionally, the text addresses constrained estimation problems that arise when linear or nonlinear economic restrictions are placed on population parameters, with examples including regression estimators and consistent estimation of contingency tables. The book also explores lesser-known connections between design-based survey sampling and other statistical fields, elucidated through the geometry of the ancient Pythagorean theorem. Beyond its practical applications, it can function as a textbook for advanced courses and a reference for researchers in statistics and empirical economics. To enhance accessibility, one chapter summarizes key statistical concepts, including regression analysis, requiring only a basic understanding of calculus and matrix algebra. Paul Knottnerus, who earned his PhD in economics in 1989, has extensive experience in statistics and methods.
