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Effects of design and error on normal convergence rates in regression problems
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  • Published: September 1990

Effects of design and error on normal convergence rates in regression problems

  • Peter Hall1 nAff2 

Probability Theory and Related Fields volume 85, pages 283–305 (1990)Cite this article

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Summary

We describe the way in which design and experimental error interact to determine convergence rates in central limit theorems for regression estimators. For example, we show that if the convergence rate in a central limit theorem for experimental errors alone isn −α, wheren is sample size and 0<α<1/2, then this rate is maintain in a central limit theorem for intercept and slope parameters if and only if the distribution generating design has finite (2+2α)'th moment. We prove that in other circumstances a careful choice of design can substantially improve convergence rates by introducing a degree of symmetry not present in the error distribution. Other results on the relationship between design and error are also derived.

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Author information

Author notes
  1. Peter Hall

    Present address: Department of Statistics, Australian National University, GPC Box 4, 2601, Canberra, ACT, Australia

Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Peter Hall

Authors
  1. Peter Hall
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Cite this article

Hall, P. Effects of design and error on normal convergence rates in regression problems. Probab. Th. Rel. Fields 85, 283–305 (1990). https://doi.org/10.1007/BF01193941

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  • Received: 15 August 1988

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01193941

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Keywords

  • Stochastic Process
  • Probability Theory
  • Convergence Rate
  • Experimental Error
  • Limit Theorem
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