Outlier resistant alternatives to the ratio estimator

Journal of the American Statistical Association

Volumn 87, Issue 420, 1992, Pages 1174-1182

  Gwet, Jean Philippe ^a   Rivest, Louis Paul ^b  

^a STATISTICS CANADA   (Canada)

^b UNIVERSITÉ LAVAL   (Canada)

Author keywords

Conditional inference; GM estimator; M estimator; Mean squared error; Robust estimation; Sample survey

Indexed keywords

EID: 31144454288     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1992.10476275     Document Type: Article

References (29)

1. Beaton, A. E., and Tukey, J. W. (1974), “The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data,” Technometrics, 16, 147–185.
2. Bellhouse, D. (1987), “Model-Based Estimation in Finite Population Sampling,” The American Statistician, 41, 260–262.
3. Boos, D. D., and Serfling, R. J. (1980), “A Note on Differentials and the CLT and LIL for Statistical Functions, With Applications to M-Estimates,” The Annals of Statistics, 8, 618–624.
4. Chambers, R. L. (1986), “Outlier Robust Finite Population Estimation,” Journal of the American Statistical Association, 81, 1063–1069.
5. Ernst, L. R. (1980), “Comparison of Estimators of the Mean Which Adjust for Large Observations,” Sankhyā, Ser. C, 42, 1–16.
6. Fernholz, L. T. (1983), Von Mises Calculus for Statistical Functionals, (Lecture Notes in Statistics 19), New York: Springer.
7. Fuller, W. A. (1991), “Simple Estimators for the Mean of Skewed Populations,” Statistica Sinica, 1, 137–158.
8. Hampel, F. R. (1974), “The Influence Curve and its Role in Robust Estimation,” Journal of the American Statistical Association, 69, 383–393.
9. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. E. (1986), Robust Statistics: The Approach Based on Influence Functions, New York: John Wiley.
10. Hidiroglou, M. H., and Srinath, K. P. (1981), “Some Estimators of the Population Total from Simple Random Samples Containing Large Units,” Journal of the American Statistical Association, 76, 690–695.
11. Huber, P. J. (1964), “Robust Estimation of a Location Parameter,” The Annals of Mathematical Statistics, 35, 73–101.
12. —— (1981), Robust Statistics, New York: John Wiley.
13. Isaki, C. T., and Fuller, W. A. (1982), “Survey Design Under the Regression Superpopulation Model,” Journal of the American Statistical Association, 77, 89–96.
14. Kish, L. (1965), Survey Sampling, New York: John Wiley.
15. Mosteller, F., and Tukey, J. W. (1977), Data Analysis and Regression, Reading, MA: Addison-Wesley.
16. Rao, C. R. (1971), “Some Aspects of Statistical Inference in Problems of Sampling from Finite Populations,” in Foundations of Statistical Inference, eds. V. P. Godambe and D. A. Sprott, Toronto: Holt, Rinehart & Winston.
17. Rao, J. N. K. (1969), “Ratio and Regression Estimators,” in New Developments in Survey Sampling, eds. N. L. Johnson and H. Smith, New York: John Wiley, pp. 213–234.
18. —— (1985), “Conditional Inferences in Survey Sampling,” Survey Methodology, 11, 15–31.
19. Rivest, L. P. (1989), “De l’Unicité des Estimateurs Robustes en Régression Quand le Paramètre d’Echelle et le Paramètre de la Régression Sont Estimés Simultanément,” Canadian Journal of Statistics, 11, 141–153.
20. Rivest, L. P., and Rouillard, E. (1991), “M-Estimators and Outlier Resistant Alternatives to the Ratio Estimator,” in Proceedings of the 1990 Symposium of Statistics Canada, pp. 271–285.
21. Royall, R. M., and Cumberland, W. G. (1981), “An Empirical Study of the Ratio Estimator and Estimators of its Variance,” Journal of the American Statistical Association, 76, 66–82.
22. Särndal, C. E. (1980), “On π-Inverse Weighting Versus Best Linear Unbiased Weighting in Probability Sampling,” Biometrika, 67, 639–650.
23. —— (1982), “Implications of Survey Design for Generalized Regression Estimation of Linear Functions,” Journal of Statistical Planning and Inference, 7, 155–170.
24. Scott, A., and Wu, C. J. (1981), “On Asymptotic Distributions of Ratio and Regression Estimators,” Journal of the American Statistical Association, 76, 98–102.
25. Searls, D. T. (1966), “An Estimator Which Reduces Large True Observations,” Journal of the American Statistical Association, 61, 1200–1204.
26. Som, R. K. (1973), A Manual of Sampling Techniques, London: Heinemann
27. Sukhatme, P. V., and Sukhatme, B. V. (1970), Sampling Theory of Surveys With Applications (2nd ed.), Rome: Food and Agriculture Organization.
28. Wright, R. L. (1983), “Finite Population Sampling with Multivariate Auxiliary Information,” Journal of the American Statistical Association, 78, 879–884.
29. Wu, C. F., and Deng, L. Y. (1983), “Estimation of the Variance of the Ratio Estimator: An Empirical Study,” in Scientific Inference, Data Analysis, and Robustness, eds. G. E. P. Box, T. Leonard, and C. F. Wu, New York: Academic Press, pp. 245–277.