Sample survey theory. Some Pythagorean perspectives
This book gives an introduction to sampling theory. It is based on the books by \textit{W.G. Cochran}, Sampling techniques. 3rd ed. (1977; Zbl 0353.62011), and \textit{C.-E. Särndal}, \textit{B. Swensson} and \textit{J. Wretman}, Model assisted survey sampling. (1992; Zbl 0742.62008). It is divided into three chapters and a prefix, which recalls elementary statistics and familiarizes the reader with the notations used in sampling theory. The titles of the parts and chapters are: I. Sampling theory and autocorrelations. Alternative approach to unequal probability sampling; A general Rho theory of survey sampling; Variance estimation for some standard designs; Multistage and cluster (sub)sampling; Systematic sampling. II. Variance estimation in complex surveys. Estimation of the sample autocorrelation coefficient; Variance approximations; A simulation study. III. Minimum variance estimators. The regression estimators revisited; General restriction estimators in multisurvey sampling; Weighting procedures. As the subtitle announces, it is a special feature of this book that the author explains the statistical quantities in terms of the geometry of Euclidean spaces as Hilbert spaces. In particular, he illustrates the projections and the related Pythagorean theorem and points out that the correlation coefficient of centered random variables is the analogue to the cosine. The book is well-written and recommendable both for graduated students and researchers.
scientific article; zbMATH DE number 1867884