Sampling Statistics

Abstract

This book developed out of a desire for a sampling course that would fit easily into a graduate program in statistics. Survey sampling is a relatively young discipline, achieving acceptance in the 1940’s and 1950’s, primarily for official statistics. As the discipline has matured, analytic use of survey data has increased inside and outside government. Also statistical models, such as those for nonresponse and for small area estimation, are now considered part of survey methodology. As a result, the overlap between survey sampling and other areas of statistics has increased, and the mutual dependence makes it important that survey sampling be an integral part of statistics. Originally, survey sampling was differentiated from other areas by the size of the data sets and by the number of estimates produced. In such a setting survey statisticians prefer techniques with broad applicability, and that require a minimum of assumptions. Procedures are sought that are nearly design unbiased, but no claim of optimality is made for a particular statistic. These standard survey techniques are introduced in Chapter One. I have adopted a tenor and notation similar to statistics texts in other specialities to make the material more accessible to those with limited exposure to survey sampling. Some of the technical material in Section 1.3 can be omitted or covered at a later point. Basic sampling concepts are introduced in a way to facilitate application of model based procedures to survey samples. Likewise, models are used in constructing estimators and in discussions of designs in Chapter Two and Chapter Three, respectively. Chapter Five is devoted to procedures, such as nonresponse adjustment and small area estimation, where models play a central role. To be comfortable with the material the reader should have completed courses in the theory of statistics and in linear regression. Survey data are now regularly used for the estimation of a parameter 0 of a subject matter model. Such estimation is discussed in Chapter Six. The problem will be familiar to most statisticians, but complex survey designs complicate the analysis. Our primary experience has been with survey samples of populations such as the residents of the state of Iowa or the land area of the United States. Thus our unconscious frame of reference will be such surveys. Likewise