Self-Normalized Processes: Limit Theory and Statistical Applications (Probability and its Applications)

✍ Scribed by Victor H. de la Peña, Tze Leung Lai, Qi-Man Shao

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 270
• Edition: 1
• Category: Library

✦ Synopsis

Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.

✦ Subjects

Математика;Теория вероятностей и математическая статистика;Теория случайных процессов;