Robust estimation of small-area means and quantiles

Australian and New Zealand Journal of Statistics

Volumn 52, Issue 2, 2010, Pages 167-186

  Tzavidis, Nikos ^a   Marchetti, Stefano ^b   Chambers, Ray ^c  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF PISA   (Italy)

^c UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

Australian farm data; Chambers Dunstan estimator; Finite population distribution function; M quantile regression; Rao Kovar Mantel estimator; Robust regression; Small area estimation; Smearing estimator

Indexed keywords

EID: 77954099502     PISSN: 13691473     EISSN: 1467842X     Source Type: Journal    
DOI: 10.1111/j.1467-842X.2010.00572.x     Document Type: Article

References (28)

1. Aragon Y, Casanova S, Chambers R, Leconte E. Conditional ordering using nonparametric expectiles. J. Off. Statist. 2005, 21:617-633.
2. Bowman AW, Hall P, Prvan T. Bandwidth selection for the smoothing of distribution functions. Biometrika 1998, 85:799-808.
3. Breckling J, Chambers RL. M-quantiles. Biometrika 1988, 75:761-771.
4. Chambers RL. Outlier robust finite population estimation. J. Amer. Statist. Assoc. 1986, 81:1063-1069.
5. Chambers RL, Dunstan R. Estimating distribution functions from survey data. Biometrika 1986, 73:597-604.
6. Chambers RL, Tzavidis N. M-quantile models for small area estimation. Biometrika 2006, 93:255-268.
7. Chambers RL, Dorfman AH, Hall P. Properties of estimators of the finite population distribution function. Biometrika 1992, 79:577-582.
8. Chambers RL, Dorfman AH, Wehrly TE. Bias robust estimation in finite populations using nonparametric calibration. J. Amer. Statist. Assoc. 1993, 88:268-277.
9. Chambers RL, Chandra H, Tzavidis N. On robust mean squared error estimation for linear predictors for domains. 2009, http://cssm.uow.edu.au/publications/UOW042821.html, Working Paper 11-09, Available from URL
10. Duan N. Smearing estimate: A nonparametric retransformation method. J. Amer. Statist. Assoc. 1983, 78:605-610.
11. Fay RE, Herriot RA. Estimation of income for small places: An application of James-Stein procedures to census data. J. Amer. Statist. Assoc. 1979, 74:269-277.
12. Henderson CR. Estimation of variance and covariance components. Biometrics 1953, 9:226-252.
13. Koenker R. Quantile Regression 2005, New York, Cambridge University Press
14. Koenker R, Bassett G. Regression quantiles. Econometrica 1978, 46:33-50.
15. Koenker R, D'Orey V. Computing regression quantiles. J. Roy. Statist. Soc. Ser. C 1987, 36:383-393.
16. Kokic P, Chambers R, Breckling J, Beare S. A measure of production performance. J. Bus. Econ. Statist. 1997, 15:445-451.
17. Li Q, Racine JS. Nonparametric Econometrics: Theory and Practice 2007, Princeton, Princeton University Press
18. Lombardía MJ, González-Manteiga W, Prada-Sánchez JM. Bootstrapping the Dorfman-Hall-Chambers-Dunstan estimator of a finite population distribution function. J. Nonpar. Statist. 2003, 16:63-90.
19. R: A Language and Environment for Statistical Computing 2008, http://www.R-project.org, R Development Core Team, R Foundation for Statistical Computing, Vienna, Austria, Avaliable from URL
20. Rao JNK. Small Area Estimation 2003, New York, Wiley
21. Rao JNK, Kovar JG, Mantel HJ. On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika 1990, 77:365-375.
22. Richardson AM. Bounded influence estimation in the mixed linear model. J. Amer. Statist. Assoc. 1997, 92:154-161.
23. Richardson AM, Welsh AH. Robust estimation in the mixed linear model. Biometrics 1995, 51:1429-1439.
24. Royall RM, Cumberland WG. Variance estimation in finite population sampling. J. Amer. Statist. Assoc. 1978, 73:351-358.
25. Sinha SK, Rao JNK. Robust small area estimation. Can. J. Statist. 2009, 37:381-399.
26. Venables WN, Ripley BD. Modern Applied Statistics with S 2002, New York, Springer
27. Wang S, Dorfman AH. A new estimator of the finite population distribution function. Biometrika 1996, 83:639-652.
28. Welsh AH, Ronchetti E. Bias-calibrated estimation from sample surveys containing outliers. J. Roy. Stat. Soc. Ser. B 1998, 60:413-428.