From Finite Sample to Asymptotic Methods in Statistics

Exact statistical inference may be employed in diverse fields of science and technology. As problems become more complex and sample sizes become larger, mathematical and computational difficulties can arise that require the use of approximate statistical methods. Such methods are justified by asymptotic arguments but are still based on the concepts and principles that underlie exact statistical inference. With this in perspective, this book presents a broad view of exact statistical inference and the development of asymptotic statistical inference, providing a justification for the use of asymptotic methods for large samples. Methodological results are developed on a concrete and yet rigorous mathematical level and are applied to a variety of problems that include categorical data, regression, and survival analyses. This book is designed as a textbook for advanced undergraduate or beginning graduate students in statistics, biostatistics, or applied statistics but may also be used as a reference for academic researchers.1. Motivation and basic tools; 2. Estimation theory; 3. Hypothesis testing; 4. Elements of statistical decision theory; 5. Stochastic processes: an overview; 6. Stochastic convergence and probability inequalities; 7. Asymptotic distributions; 8. Asymptotic behavior of estimators and tests; 9. Categorical data models; 10. Regression models; 11. Weak convergence and Gaussian processes.