JSM 2005 - Toronto

Abstract #304680

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Activity Number: 401
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #304680
Title: Developments in Weak Convergence
Author(s): John Fresen*+
Companies: University of Limpopo
Address: PO Box 107, Pretoria, 0204, South Africa
Keywords: Convergence ; Non-measurable ; Empirical ; Processes
Abstract:

Perhaps the first weak convergence result was due to de Moive, who derived the normal approximation to the binomial distribution in 1733. In 1785, Laplace derived the central limit theorem for a discrete distribution via the characteristic function (Hald 1998). However, the major developments in weak convergence took place in the second quarter of the last century. In 1968, Billingsley published his classical text Convergence of Probability Measures that provided a summary of the developments in weak convergence up to the 1960s. In 1996, van der Vaart and Wellner published their text, Weak Convergence and Empirical Processes, which discussed the weak convergence of nonmeasurable functions. In this paper, we discuss recent developments in weak convergence.

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