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Incomplete data in sample surveys. Volume 2: Theory and bibliographies. (English) Zbl 0561.62008

Panel on Incomplete Data, Committee on National Statistics, Commission on Behavioral and Social Sciences and Education, National Research Council. New York - London etc.: Academic Press (Harcourt Brace Jovanovich, Publishers). XXV, 579 p. $ 50.00 (1983).
[For Vol. I see the preceding review, Zbl 0561.62007.]
This volume presents the theory involved with incomplete data in sample surveys. Part I consists of an introduction to the volume and in Chapter 2 appears one of the last works of the late Professor W. G. Cochran. It presents the history of the treatment of incomplete data and notes on the different parts of this volume. This chapter, I think, is a key one.
Part II is dedicated to the presentation of techniques for solving for the incompleteness of data. The theory that sustains the technique of callbacks and substitution methods is summarized and quota sampling’s perfomance is empirically compared with the corresponding probabilistic models. The randomized response technique is suggested by L. Emrich as a method for diminishing nonresponse rates. The need of more empirical evaluations is fixed.
The use of auxiliary information for obtaining the non available data is faced in the paper of M. G. Sirken. He develops a model for obtaining the value of the variables of nonrespondents by the use of criteria given by the respondents. A graph is generated and the analysis of the estimation’s performance is made using this frame. Part III deals with the problem of subsampling the stratum of the nonrespondents. Chapter 10 presents the inference approach based on randomization and Chapter 11 presents the Bayesian one.
Part IV contains four chapters. It is devoted to the problem of weighting and imputation methods. D. B. Rubin presents the approach based on randomization principle and a model-oriented Bayesian alternative. The notation used in this part is introduced and these approaches are compared in the case of full response and in that of nonresponse. Chapter 13, due to H. L. Oh and F. J. Schreun, studies the performance of different alternative estimators when missing observations are present in the data and weighting adjustment is used for unit nonresponse. A probability based response mechanism is introduced for simple random sampling and used as a frame for dealing with the comparisons. Hot-deck and imputation procedures are presented in Chapters 14 and 15.
Part V deals with imputation methodologies which are present in four chapters written by R. Platek and G. B. Gray. It gives a complete account of the state of the art. The performance of four imputation methods is analyzed when Horvitz-Thompson type estimators are used. An hypothetical example illustrates the effect of the imputation methods in biases and variances.
Part VI is formed by three chapters which have been written by R. J. A. Little. The role of superpopulation models is fixed in this part. The basic theoretical frame is established and maximum likelihood estimators are obtained under the assumption that observations are randomly missed. A nonresponse model is developed and the ignorability of sampling designs for deriving maximum likelihood estimators is supported by eight sufficiency conditions. Examples are given. Problems related with contingency tables and a Bayesian approach to nonresponse bias estimation are presented. Part VII gives an extensive and selected bibliography.
I think that the reading of this volume provides the possibility of obtaining a complete account of the present state of the art of the theory of incomplete data in sample surveys.
Reviewer: C.N.Bouza

MSC:

62D05 Sampling theory, sample surveys
62-06 Proceedings, conferences, collections, etc. pertaining to statistics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62G05 Nonparametric estimation
62-07 Data analysis (statistics) (MSC2010)

Citations:

Zbl 0561.62007