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Mathematics - Probability Theory and Stochastic Processes | Sample Survey Theory - Some Pythagorean Perspectives

Sample Survey Theory

Some Pythagorean Perspectives

Knottnerus, Paul

2003, XX, 420 p.

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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.

Content Level » Research

Keywords » Estimator - Multinomial distribution - Normal distribution - Random variable - Regression analysis - Survey Sampling - Variance - correlation

Related subjects » Probability Theory and Stochastic Processes - Social Sciences & Law - Statistical Theory and Methods

Table of contents 

Introduction and Outline of the Book * Elementary Statistics * Alternative Approach to Unequal Probability Sampling * A General Rho Theory on Survey Sampling * Variance Estimation for Some Standard Designs * Multistage and Cluster (Sub)Sampling * Systematic Sampling * Estimation of the Sampling Autocorrelation Coefficient * Variance Approximations * A Simulation Study * The Regression Estimator Revisited * General Restriction Estimator in Multisurvey Sampling * Weighting Procedures

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