Self-Normalized Processes

This insightful work, Self-Normalized Processes, explores recent advancements in self-normalized processes and their applications in statistics and probability.

The book Self-Normalized Processes delves into the recent advancements in the field of self-normalized processes, which are crucial in various probabilistic and statistical analyses. It highlights significant topics such as self-normalized large and moderate deviations, as well as the laws of iterated logarithms specifically for self-normalized martingales. These processes have become increasingly relevant, especially given their applications in statistical inference and central limit theorems.

Self-normalized processes are frequently encountered in statistical studies, with a notable example being Student's t-statistic, introduced by Gosset in 1908. Despite their common occurrence, the complexity and non-linear characteristics of these processes have historically hindered their theoretical development. However, this volume illuminates the recent breakthroughs that have propelled the understanding and application of self-normalized processes forward, making it a timely resource for researchers and practitioners alike.

This publication stands out as the first comprehensive treatment of the theory and applications of self-normalization. By systematically addressing the advancements in this area, Self-Normalized Processes not only provides a solid foundation for understanding these processes but also encourages further exploration and application in various statistical contexts.