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Behavior of elemental sets in regression

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  • Olive, David J.
  • Hawkins, Douglas M.

Abstract

Elemental sets are used to produce trial estimates b of the regression coefficients [beta]. If b0 minimizes [short parallel]b-[beta][short parallel] among all elemental fits b, then [short parallel]b0-[beta][short parallel]=OP(n-1), regardless of the criterion used. For any estimator bA, [short parallel]bA-[beta][short parallel] is at best OP(n-1/2). Hence restricting fits to elemental introduces asymptotically negligible error.

Suggested Citation

  • Olive, David J. & Hawkins, Douglas M., 2007. "Behavior of elemental sets in regression," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 621-624, March.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:6:p:621-624
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    References listed on IDEAS

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    1. Hawkins D. M. & Olive D. J., 2002. "Inconsistency of Resampling Algorithms for High-Breakdown Regression Estimators and a New Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 136-159, March.
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    Cited by:

    1. Hawkins, Douglas M. & Khan, Dost Muhammad, 2009. "A procedure for robust fitting in nonlinear regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4500-4507, October.
    2. Gabriel Okasa & Kenneth A. Younge, 2022. "Sample Fit Reliability," Papers 2209.06631, arXiv.org.

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