Journal of Theoretical Probability

, Volume 9, Issue 3, pp 765–796 | Cite as

A Berry-Esséen bound for student's statistic in the non-I.I.D. case

  • V. Bentkus
  • M. Bloznelis
  • F. Götze
Article

Abstract

We establish a Berry-Esséen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esséen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.

Key Words

Student's statistic Berry-Esséen bound non-identically distributed random variables convergence rate Central Limit Theorem selfnormalized sums 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. Bentkus
    • 1
  • M. Bloznelis
    • 2
  • F. Götze
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeld 1Germany
  2. 2.Department of MathematicsVilnius UniversityVilniusLithuania

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