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Exponential Type Estimates of Probabilities

In: Probability Inequalities

Author

Listed:
  • Zhengyan Lin

    (Zhejiang University, Department of Mathematics)

  • Zhidong Bai

    (Northeast Normal University, School of Mathematics and Statistics
    National University of Singapore, Department of Statistics and Applied Probabilty)

Abstract

Exponential rate is the best in convergence in probability. Such inequalities are important when investigating the law of large numbers and the law of iterated logarithm. Some of such inequalities are well known and frequently employed in statistics and probability, such as Hoeffding, Bernstein, Bennett and Kolmogorov inequalities. These inequalities can be found in most textbooks on limiting theorems, such as (1977), (1995). Some new inequalities will be referenced therein.

Suggested Citation

  • Zhengyan Lin & Zhidong Bai, 2010. "Exponential Type Estimates of Probabilities," Springer Books, in: Probability Inequalities, chapter 0, pages 67-83, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-05261-3_7
    DOI: 10.1007/978-3-642-05261-3_7
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