Estimation of variance components with high breakdown point and high efficiency

Biometrika

Volumn 88, Issue 2, 2001, Pages 353-366

  Müller, Christine H ^a   Uhlig, Steffen ^b  

^a UNIVERSITY OF OLDENBURG   (Germany)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Asymptotic normality; Breakdown point; Interlaboratory test; Q estimator; Robust estimation; Variance component model

Indexed keywords

EID: 0038442187     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/88.2.353     Document Type: Article

References (24)

1. BEDNARSKI, T. & MüLLER, C. H. (2001). Optimal bounded influence regression and scale A/-estimators. Statistics. To appear.
2. BEDNARSKI, T. & ZONTEK, S. (1996). Robust estimation of parameters in a mixed unbalanced model. Ann. Statist. 24, 1493-510.
3. DONOHO, D. L. & HUBER, P. J. (1983). The notion of breakdown point. In A Festschrift for Erich L. Lehmatm, Ed. P. J. Bickel, K. A. Doksum and J. L. Hodges, Jr., pp. 157-84. Belmont, CA: Wadsworth.
4. ELLIS, S. P. & MORGENTHALER, S. (1992). Leverage and breakdown in L! regression. J. Am. Statist. Assoc. 87, 143-8.
5. FELLNER, W. H. (1986. Robust estimation of variance components. Technometrics 28, 51-60.
6. GHOSH, J. K. (1971). A new proof of the Bahadur representation of quantiles and an application. Ann. Math. Statist. 42, 1957-61.
7. HE, X., JUREèKOVâ, J., KOENKER, R. & PORTNOY, S. (1990). Tail behavior of regression estimators and their breakdown points. Econometrica 58, 1195-214.
8. HUGGINS, R. M. (1993a). A robust approach to the analysis of repeated measures. Biometrics 49, 715-20.
9. HUGGINS, R. M. (1993b). On the robust analysis of variance components models for pedigree data. Anst. J. Statist. 35, 43-57.
10. ISO-5725-2 (1992). Accuracy (Triteness and Precision) of Test Measurements. Geneva: International Organisation for Standardisation.
11. LISCHER, P. (1996). Robust statistical methods in interlaboratory analytical studies. In Robust Statistics, Data Analysis, and Computer Intensive Methods, Ed. H. Rieder, pp. 251-64. New York: Springer.
12. MüLLER, C. H. (1997). Robust Planning and Analysis of Experiments, Lecture Notes in Statistics 124. New York: Springer.
13. MüLLER, C. H. (2000). Asymptotic normality and efficiency of variance components estimators with high breakdown points. Disc. Math.-Algeb. Stoch. Meth. 20, 85-95.
14. RICHARDSON, A. M. (1997). Bounded influence estimation in the mixed linear model. J. Am. Statist. Assoc. 92, 154-61.
15. RICHARDSON, A. M. & WELSH, A. H. (1995). Robust restricted maximum likelihood in mixed linear models. Biometrics 51, 1429-39.
16. ROCKE, D. M. (1983). Robust statistical analysis of interlaboratory studies. Biometrika 70, 421-31.
17. ROCKE, D. M. (1991). Robustness and balance in the mixed model. Biometrics 47, 303-9.
18. ROUSSEEUW, P. J. & CROUX, C. (1992). Explicit scale estimators with high breakdown point. In Lt-Statistical Analysis and Related Methods, Ed. Y. Dodge, pp. 77-92. Amsterdam: North-Holland.
19. ROUSSEEUW, P. J. & CROUX, C. (1993). Alternatives to the median absolute deviation. J. Am. Statist. Assoc. 88, 1273-83.
20. ROUSSEEUW, P. J. & LEROY, A. M. (1987). Robust Regression and Outlier Detection. New York: John Wiley.
21. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. New York: John Wiley.
22. SERFLING, R. J. (1984). Generalized L-, M-, and K-statistics. Ann. Statist. 12, 76-86.
23. UHLIG, S. (1997). Robust estimation of variance components with high breakdown point in the 1-way random effect model. In Industrial Statistics. Aims and Computational Aspects, Ed. C. P. Kitsos and L. Edler, pp. 65-73. Heidelberg: Physica-Verlag.
24. UHLIG, S. & LISCHER, P. (1998). Statistically-based performance characteristics in laboratory performance studies. Analyst 123, 167-72.