Advanced Sampling Theory with Applications: How Michael ‘selected’ Amy is a comprehensive expose of basic and advanced sampling techniques along with their applications in the diverse fields of science and technology. This book is a multi-purpose document. It can be used as a text by teachers, as a reference manual by researchers, and as a practical guide by statisticians. It covers 1165 references from different research journals through almost 1900 citations across 1194 pages, a large number of complete proofs of theorems, important results such as corollaries, and 324 unsolved exercises from several research papers. It includes 159 solved, data-based, real life numerical examples in disciplines such as Agriculture, Demography, Social Science, Applied Economics, Engineering, Medicine, and Survey Sampling. These solved examples are very useful for an understanding of the applications of advanced sampling theory in our daily life and in diverse fields of science. An additional 173 unsolved practical problems are given at the end of the chapters. University and college professors may find these useful when assigning exercises to students. Each exercise gives exposure to several complete research papers for researchers/students. The data-based problems show statisticians how to select a sample and obtain estimates of parameters from a given population by using different sampling strategies, systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling. Derivations of calibration weights from the design weights under single phase and two-phase sampling have been provided for simple numerical examples. These examples will be useful to understand the meaning of benchmarks to improve the design weights. These examples also explain the background of well-known scientific computer packages like CALMAR, GES, SAS, STATA, and SUDAAN etc., used to generate calibration weights by most organizations in the public and private sectors. The ideas of hot deck, cold deck, mean method of imputation, ratio method of imputation, compromised imputation, and multiple imputations have been explained with very simple numerical examples. Simple examples are also provided to understand Jackknife variance estimation under single phase, two-phase [or random non-response by following Sitter (1997)] and multi-stage stratified designs. This book also covers, in a very simple and compact way, many new topics not yet available in any book on the international market. A few of these interesting topics are: median estimation under single phase and two-phase sampling; difference between low level and higher level calibration approach; calibration weights and design weights; estimation of parametric functions; hidden gangs in finite populations; compromised imputation; variance estimation using distinct units; general class of estimators of population mean and variance; wider class of estimators of population mean and variance; power transformation estimators; and estimators based on the mean of non-sampled units of the auxiliary character.
