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Robust estimation in finite population sampling

Malay Ghosh

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Abstract

The paper proposes some robust estimators of the finite population mean. Such estimators are particularly suitable in the presence of some outlying observations. Included as special cases of our general result are robust versions of the ratio estimator and the Horvitz-Thompson estimator. The robust estimators are derived on the basis of certain predictive influence functions.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 116-122

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058268

Digital Object Identifier
doi:10.1214/193940307000000086

Subjects
Primary: 62F35: Robustness and adaptive procedures 62D05: Sampling theory, sample surveys
Secondary: 62F15: Bayesian inference

Keywords
Horvitz-Thompson estimator influence functions predictive ratio estimator

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Ghosh, Malay. Robust estimation in finite population sampling. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 116--122, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000086. https://projecteuclid.org/euclid.imsc/1207058268


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References

  • [1] Amari, S. (1982). Differential geometry of curved exponential families – curvatures and information loss. Ann. Statist. 10 357–387.
  • [2] Basu, D. (1971). An essay on the logical foundations of survey sampling, part one. In Foundations of Statistical Inference (V. P. Godambe and D. A. Sprott, eds.) 203–242. Holt, Rinehart and Winston, Toronto.
  • [3] Bhattacharyya, A. K. (1943). On a measure of divergence between two statistical populations defined by their probability distributions. Bull. Calcutta Math. Soc. 35 99–109.
  • [4] Chambers, R. L. (1986). Outlier robust finite population estimation. J. Amer. Statist. Assoc. 81 1063–1069.
  • [5] Cressie, N. and Read, T. R. C. (1984). Multinomial goodness-of-fit tests. J. Roy. Statist. Soc. Ser. B 46 440–464.
  • [6] Efron, B. and Morris, C. (1971). Limiting the risk of Bayes and empirical Bayes estimators. I. The Bayes case. J. Am. Statist. Assoc. 66 807–815.
  • [7] Efron, B. and Morris, C. (1972). Limiting the risk of Bayes and empirical Bayes estimators. II. The empirical Bayes case. J. Amer. Statist. Assoc. 67 130–139.
  • [8] Feller, W. (1957). An Introduction to Probability Theory and its Applications, V1, 2nd ed. Wiley, New York.
  • [9] Ghosh, M. and Sinha, B. K. (1990). On the Consistency between model- and design-based estimators in survey sampling. Comm. Statist. Theory Methods 19 689–702.
  • [10] Gwet, J-P. and Rivest, L-P. (1992). Outlier resistant alternatives to the ratio estimator. J. Amer. Statist. Assoc. 87 1174–1182.
  • [11] Hellinger, E. (1909). Neue Begründung der Theorie Quadratischen Formen von unendlichen vielen Veränderlichen. J. Reine und Angewandte Mathematik 136 210-V-271.
  • [12] Hampel, F. R. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69 383–393.
  • [13] Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics. The Approach Based on Influence Functions. Wiley, New York.
  • [14] Huber, P. J. (1981). Robust Statistics. Wiley, New York.
  • [15] Johnson, W. and Geisser, S. (1982). Assessing the predictive influence of observations. In Essays in Honor of C.R. Rao (G. Kalianpur, P. R. Krishnaiah and J. K. Ghosh, eds.) 343–358. North-Holland, Amsterdam.
  • [16] Johnson, W. and Geisser, S. (1983). A predictive view of the detection and characterization of influential observations in regression analysis. J. Amer. Statist. Assoc. 78 137–144.
  • [17] Johnson, W. and Geisser, S. (1985). Estimative influence measures for the multivariate general linear model. J. Statist. Plann. Inference 11 33–56.
  • [18] Jureckova, J. and Sen, P. K. (1996). Robust Statistical Procedures: Asymptotics and Interrelations. Wiley, New York.
  • [19] Royall, R. M. (1970). On finite population sampling theory under certain linear regression models. Biometrika 57 377–387.