Rabi N. Bhattacharya pp 3-13

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Contributions of Rabi Bhattacharya to the Central Limit Theory and Normal Approximation

  • Peter Hall
Chapter

Abstract

Rabi Bhattacharya has made signal contributions to central limit theory and normal approximation, particularly for sums of independent random vectors. His monograph in the area (Bhattacharya and Ranga Rao 1976) has become a classic, its importance being so great that it has had significant influence on mathematical statistics as well as probability. The methods developed in that monograph led to Bhattacharya and Ghosh’s (1978) seminal account of general Edgeworth expansions under the smooth function model, as it is now commonly called. That article had a profound influence on the development of bootstrap methods, not least because it provided a foundation for influential research that enabled different bootstrap methods to be compared. At a vital time in the evolution of bootstrap methods, it led to an authoritative and enduring assessment of many of the bootstrap’s important contributions.

Keywords

Asymptotic expansion Berry-Esseen bound Bootstrap Diffusion Edgeworth expansion Markov model Moment condition Oscillation Rates of convergence Smooth function model Smoothing lemma 

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Peter Hall
    • 1
  1. 1.SydneyAustralia

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