Sample Survey Theory

Some Pythagorean Perspectives

Paul Knottnerus (Autor)

Buch | Softcover

420 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2003
Springer-Verlag New York Inc.
978-1-4419-2988-4 (ISBN)

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This volume deals primarily with the classical question of how to draw conclusions about the population mean of a variable, given a sample with observations on that variable. Another classical question is how to use prior knowledge of an economic or definitional relationship between the popu lation means of several variables, provided that the variables are observed in a sample. The present volume is a compilation of two discussion papers and some additional notes on these two basic questions. The discussion papers and notes were prepared for a 15-hour course at Statistics Nether lands in Voorburg in February 2000. The first discussion paper is entitled "A Memoir on Sampling and Rho, the Generalized Intrasample Correlation Coefficient" (1999). It describes a new approach to the problem of unequal probability sampling. The second discussion paper "The General Restric tion Estimator" (2000), deals with the problem of how to find constrained estimators that obey a given set of restrictions imposed on the parameters to be estimated. Parts I and II of the volume provide a novel and systematic treatment of sampling theory considered from the angle of the sampling autocorrelation coefficient p (rho). The same concept plays an important role in the analysis of time series. Although this concept is also well known in sampling theory, for instance in cluster sampling and systematic sampling, generalizations of p for an arbitrary sampling design are to my knowledge not readily found in the literature.

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.

Erscheint lt. Verlag	6.12.2010
Reihe/Serie	Springer Series in Statistics
Zusatzinfo	XX, 420 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Themenwelt	Sozialwissenschaften ► Soziologie ► Empirische Sozialforschung
ISBN-10	1-4419-2988-6 / 1441929886
ISBN-13	978-1-4419-2988-4 / 9781441929884
Zustand	Neuware