Sample Survey Theory

Some Pythagorean Perspectives
Softcover Nachdruck of hardcover 1. Auflage 2003
ISBN: 978-1-4419-2988-4
Verlag: Springer

Buch, Englisch, 420 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 663 g

Reihe: Springer Series in Statistics

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. This volume will be useful for survey practitioners faced with complex surveys.

Zielgruppe

Research

Autoren/Hrsg.

Knottnerus, Paul

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

1 Introduction and Outline of the Book.- 2 Elementary Statistics.- 2.1 Definitions of population parameters.- 2.2 Random variables and the normal distribution.- 2.3 Conditional probabilities and stochastic independence.- 2.4 The binomial and multinomial distributions.- 2.5 Classical sampling.- 2.6 The hypergeometric distribution.- 2.7 Multivariate analysis and multiple regression.- 2.8 Minimum variance estimation of random variables.- 2.9 Kalman-like update equations and an update paradigm.- 2.10 The Cramér-Rao inequality and other inequalities.- 2.11 Some additional algebra.- Appendix 2.A Moore-Penrose Inverses and Kronecker Products.- Appendix 2.B The Discrete Kalman Filter.- I Sampling Theory and Autocorrelations.- 3 Alternative Approach to Unequal Probability Sampling.- 4 A General Rho Theory on Survey Sampling.- 5 Variance Estimation for Some Standard Designs.- 6 Multistage and Cluster (Sub)Sampling.- 7 Systematic Sampling.- II Variance Estimation in Complex Surveys.- 8 Estimation of the Sampling Autocorrelation ?z.- 9 Variance Approximations.- 10 A Simulation Study.- III Minimum Variance Estimators.- 11 The Regression Estimator Revisited.- 12 General Restriction Estimator in Multisurvey Sampling.- 13 Weighting Procedures.- References.