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The asymptotics of the least trimmed absolute deviations (LTAD) estimator

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  • Tableman, Mara

Abstract

The method of least trimmed absolute deviations (LTAD) is formally treated. This method, like the LMS and LTS methods of Rousseeuw (1987), uses a criterion function that is calculated over half-samples. A population analogue is defined and its properties are discussed. The asymptotic properties of the LTAD estimator are derived. It is shown to be consistent and asymtotically normal. It is also shown to be, with asymptotic certainty, the midpoint of the interval spanned by the selected half-sample. Further, it is shown how to construct a distribution-free tolerance interval for predicting the next observation. Finally, comparisons of the asymtotic variances for the LTS and LTAD are made and recommendations are given.

Suggested Citation

  • Tableman, Mara, 1994. "The asymptotics of the least trimmed absolute deviations (LTAD) estimator," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 387-398, April.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:5:p:387-398
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    Citations

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    Cited by:

    1. Cizek, P., 2007. "General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Other publications TiSEM eeccf622-dd18-41d4-a2f9-b, Tilburg University, School of Economics and Management.
    2. G. Zioutas & C. Chatzinakos & T. D. Nguyen & L. Pitsoulis, 2017. "Optimization techniques for multivariate least trimmed absolute deviation estimation," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 781-797, October.
    3. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    4. Nathan Sudermann-Merx & Steffen Rebennack, 2021. "Leveraged least trimmed absolute deviations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 809-834, September.
    5. Olive, David J. & Hawkins, Douglas M., 2003. "Robust regression with high coverage," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 259-266, July.
    6. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
    7. Neykov, N.M. & Čížek, P. & Filzmoser, P. & Neytchev, P.N., 2012. "The least trimmed quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1757-1770.
    8. C. Chatzinakos & L. Pitsoulis & G. Zioutas, 2016. "Optimization techniques for robust multivariate location and scatter estimation," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1443-1460, May.
    9. Furno, Marilena, 1998. "Estimating the variance of the LAD regression coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 11-26, March.

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