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Influence of design on the rate of convergence to normality in L1 regression

Published online by Cambridge University Press:  28 June 2011

Peter Hall  and
A. H. Welsh
Peter Hall
Affiliation:
Statistics Department, Australian National University, Canberra, Australia
A. H. Welsh
Affiliation:
Statistics Department, Australian National University, Canberra, Australia
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Abstract

We provide a concise account of the influence of design variables on the convergence rate in an L1 regression problem. In particular, we show that the convergence rate may be characterized precisely in terms of third and fourth moments of the design variables. This result leads to necessary and sufficient conditions on the design for the Berry-Esseen rate to be achieved. We also show that a moment condition on the error distribution is necessary and sufficient for a non-uniform Berry-Esseen theorem, and that an Edgeworth expansion is possible if the design points are not too clumped.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 355 - 368
Copyright
Copyright © Cambridge Philosophical Society 1989

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