Asymptotic normality and efficiency of variance components estimators with high breakdown points

Christine H. Müller

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 1, page 85-95
  • ISSN: 1509-9423

Abstract

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For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of the maximum likelihood estimators.

How to cite

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Christine H. Müller. "Asymptotic normality and efficiency of variance components estimators with high breakdown points." Discussiones Mathematicae Probability and Statistics 20.1 (2000): 85-95. <http://eudml.org/doc/287622>.

@article{ChristineH2000,
abstract = {For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of the maximum likelihood estimators.},
author = {Christine H. Müller},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {variance component model; robust estimation; Q estimator; asymptotic normality},
language = {eng},
number = {1},
pages = {85-95},
title = {Asymptotic normality and efficiency of variance components estimators with high breakdown points},
url = {http://eudml.org/doc/287622},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Christine H. Müller
TI - Asymptotic normality and efficiency of variance components estimators with high breakdown points
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 1
SP - 85
EP - 95
AB - For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of the maximum likelihood estimators.
LA - eng
KW - variance component model; robust estimation; Q estimator; asymptotic normality
UR - http://eudml.org/doc/287622
ER -

References

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  1. [1] T. Bednarski and S. Zontek, Robust estimation of parameters in a mixed unbalanced model, Ann. Statist. 24 (1996), 1493-1510. Zbl0878.62024
  2. [2] W.H. Fellner, Robust estimation of variance components, Technometrics 28 (1986), 51-60. Zbl0597.62018
  3. [3] J.K. Ghosh, A new proof of the Bahadur representation of quantiles and an application, Ann. Math. Statist. 42 (1971), 1957-1961. Zbl0235.62006
  4. [4] R.M. Huggins, A robust approach to the analysis of repeated measures, Biometrics 49 (1993a), 715-720. 
  5. [5] R.M. Huggins, On the robust analysis of variance components models for pedigree data, Austral. J. Statist. 35 (1993b), 43-57. Zbl0772.62062
  6. [6] P. Lischer, Robust statistical methods in interlaboratory analytical studies, Robust Statistics, Data Analysis, and Computer Intensive Methods, ed. H. Rieder, Springer 1996, 251-264. Zbl0839.62033
  7. [7] A.M. Richardson and A.H. Welsh, Robust restricted maximum likelihood in mixed linear models, Biometrics 51 (1995), 1429-1439. Zbl0875.62313
  8. [8] D.M. Rocke, Robust statistical analysis of interlaboratory studies, Biometrika 70 (1983), 421-431. 
  9. [9] D.M. Rocke, Robustness and balance in the mixed model, Biometrics 47 (1991), 303-309. 
  10. [10] P.J. Rousseeuw and C. Croux, Explicit scale estimators with high breakdownpoint, L1-Statistical Analysis and Related Methods, ed. Y. Dodge, North-Holland, Amsterdam 1992, 77-92. 
  11. [11] P.J. Rousseeuw and C. Croux, Alternatives to the median absolute deviation, J. Amer. Statist. Assoc. 88 (1993), 1273-1283. Zbl0792.62025
  12. [12] R.J. Serfling, Approximation Theorems of Mathematical Statistics, John Wiley, New York 1980. Zbl0538.62002
  13. [13] R.J. Serfling, Generalized L-, M-, and R-statistics, Ann. Statist. 12 (1984), 76-86. 
  14. [14] S. Uhlig, Entwicklung und DV-mäßige Implementierung eines Programmes zur Auswertung von analytischen Laborvergleichsuntersuchungen gemäß international harmonisierender Protokolle: Mathematisch-statistische Konzeption, Research Report, Bundesinstitut für gesundheitlichen Verbraucherschutz und Veterinärmedizin 1995. 
  15. [15] S. Uhlig, Robust estimation of variance components with high breakdown point in the 1-way random effect model, Industrial Statistics, Aims and Computational Aspects, eds. C.P. Kitsos, L. Edler, Physica-Verlag, Heidelberg 1997, 65-73. 

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