Self-Normalized Processes

Limit Theory and Statistical Applications

  • Victor H. de la Peña
  • Tze Leung Lai
  • Qi-Man Shao

Part of the Probability and its Applications book series (PIA)

About this book


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.


Bootstrapping Likelihood Random variable bootstrap calculus large and moderate deviations law of the iterated logarithm self-normalization sequential analysis studentized U-statistic t-statistic

Authors and affiliations

  • Victor H. de la Peña
    • 1
  • Tze Leung Lai
    • 2
  • Qi-Man Shao
    • 3
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of StatisticsStanford UniversityStanfordUSA
  3. 3.Department of MathematicsHong Kong University of Science and TechnologyKowloonPeoples Republic of China

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