Sample survey theory. Some Pythagorean perspectives
type: Item
instance of: scholarly article
title: Sample survey theory. Some Pythagorean perspectives
zbMATH Open document ID: 1015.62002
author: Paul Knottnerus
published in: Springer Series in Statistics
publication date: 2003-02-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 62-02
zbMATH DE Number: 1867884
zbMATH Keywords: simple random sampling
zbMATH Keywords: Poisson sample
zbMATH Keywords: Bernoulli sampling
zbMATH Keywords: stratified sampling
zbMATH Keywords: poststratification
zbMATH Keywords: regression estimator
zbMATH Keywords: variance estimator
zbMATH Keywords: multistage sampling
zbMATH Keywords: autocorrelation coefficient
reviewed by: Klaus Thomas Hess
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1867884