Large Sample Methods in Statistics: An Introduction with Applications
"Large Sample Methods in Statistics" bridges the gap between sound theoretical developments and fruitful methodological adaptations in practice by ... Show synopsis "Large Sample Methods in Statistics" bridges the gap between sound theoretical developments and fruitful methodological adaptations in practice by providing a solid justification for standard asymptotic statistical methods at an intermediate mathematical level. It not only contains a unified survey of standard large sample theory but also provides access to more complex statistical models. Major emphasis is given to applications in such fields as biostatistics, public health, medical statistics, environmental sciences, industrial statistics, quality control, operations research and systems analysis, econometrics, management, psychometry and sociology. The basic concepts of stochastic convergence, convergence in distribution, convergence of moments, and the related results are laid down elaborately. The role of the sample distribution function and its intricate relation to order statistics is examined in the light of these concepts. Specific applications to large sample estimation theory and testing of statistical hypotheses both in traditional linear and categorical data models are considered along with an introduction to generalized linear models. Recent developments on weak convergence theory are outlined and their fundamental role in modern large sample theory is highlighted. This book can be used as the basis of a one term course for upper level undergraduates and graduates in statistics, biostatistics, and applied statistics. Researchers and professionals should find it useful not only as a reference book but also as an essential resource on the theory needed to understand the methodology required for their work.