1Universidad Santo Tomás, Facultad de Estadística, Centro de Investigaciones y Estudios Estadísticos (CIEES), Bogotá, Colombia. Director. Email: hugogutierrez@usantotomas.edu.co
2Colorado State University, Department of Statistics, Fort Collins, USA. Professor and Chair. Email: jbreidt@stat.colostate.edu
This paper presents a new regression estimator for the total of a population created by means of the minimization of a measure of dispersion and the use of the Wilcoxon scores. The use of a particular nonparametric model is considered in order to obtain a model-assisted estimator by means of the generalized difference estimator. First, an estimator of the vector of the regression coefficients for the finite population is presented and then, using the generalized difference principles, an estimator for the total a population is proposed. The study of the accuracy and efficiency measures, such as design bias and mean square error of the estimators, is carried out through simulation experiments.
Key words: Finite population, Regression estimator, Wilcoxon score.
Este artículo presenta un nuevo estimador de regresión para el total poblacional de una característica de interés, creado por la minimización de una medida de dispersión y el uso de los puntajes de Wilcoxon. Se considera el uso de un modelo no paramétrico con el fin de obtener un estimador asistido por modelos, que surge del estimador de diferencia gene ralizada. En primer lugar, se presenta un nuevo estimador del vector de coeficientes de regresión y luego, haciendo uso de los principios del estimador de diferencia generalizada, se propone un estimador para el total poblacional. El estudio de las medidas de precisión y eficiencias, como el sesgo y el error cuadrático medio, se lleva a cabo mediante experimentos de simulación.
Palabras clave: estimador de regresión, población finita, puntaje de\\Wilcoxon.
Texto completo disponible en PDF
References
]]>1. Breidt, F. J. & Opsomer, J. D. (2000), `Local Polynomial Regression Estimators in Survey Sampling´, The Annals of Statistics 28, 1026-1053. [ Links ]
2. Cassel, C. M., Särndal, C. E. & Wretman, J. (1976a), `Some Results on Generalized Difference Estimation and Generalized Regression Estimation for Finite Populations´, Biometrika 63, 615-620. [ Links ]
3. Cassel, C. M., Särndal, C. E. & Wretman, J. (1976b), Foundations of Inference in Survey Sampling, Wiley, New York, United States. [ Links ]
4. Chen, J. & Qin, J. (1993), `Empirical Likelihood Estimation for Finite Populations and the Efectivene Usage of Auxiliary Information´, Biometrika 80, 107-116. [ Links ]
5. Deville, J. C. & Särndal, C. E. (1992), `Calibration Estimators in Survey Sampling´, Journal of the American Statistical Association 87, 376-382. [ Links ]
6. Draper, D. (1988), `Rank-Based Robust Analysis of Linear Models I. Exposition and Review´, Statistical Science 3, 239-257. [ Links ]
7. Hettmansperger, T. P. (1984), Statistical Inference Based on Ranks, Wiley, New York, United States. [ Links ]
8. Hettmansperger, T. P. & McKean, J. W. (1998 address London, Great Britain), Robust Nonparametric Statistical Methods, Arnold. [ Links ]
9. Horvitz, D. G. & Thompson, D. J. (1952), `A Generalization of Sampling Without Replacement from a Finite Universe´, Journal of the American Statistical Association 47, 663-685. [ Links ]
10. Isaki, C. T. & Fuller, W. A. (1982), `Survey Design under the Regression Superpopulation Model´, Journal of the American Statistical Association 767, 89-96. [ Links ]
11. Jaeckel, L. (1972), `Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals´, The Annals of Mathematical Statistics 43, 1449-1458. [ Links ]
12. Jurecková, J. (1971), `Nonparametric Estimate of Regression Coefficients´, The Annals of Mathematical Statistics 42, 1328-1338. [ Links ]
13. Lohr, S. (1999), Sampling: Design and Analysis, Duxbury Press, California, United States. [ Links ]
14. Särndal, C. E. (1980), `On \pi-inverse Weighting Versus best Linear Unbiased Weighting in Probability Sampling´, Biometrika 67, 639-650. [ Links ]
15. Särndal, C. E., Swensson, B. & Wretman, J. (1989), `The Weighted Residual Technique for Estimating the Variance of the General Regression Estimator of the Finite Popoulation Total´, Biometrika 76, 527-537. [ Links ]
16. Särndal, C. E., Swensson, B. & Wretman, J. (1992), Model Assisted Survey Sampling, Springer, New York, United States. [ Links ]
17. Team, R. D. C. (2007), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. [ Links ]
18. Terpstra, J. F. & McKean, J. W. (2005), `Rank-based analyses of linear models using R´, Journal of Statistical Software 14, 1-26. [ Links ]
19. Wu, C. (2003), `Optimal Calibration Estimators in Survey Sampling´, Biometrika 90, 937-951. [ Links ]
20. Wu, C. & Sitter, R. R. (2001), `A Model Calibration Approach to Using Complete Auxiliary Information from Survey Data´, Journal of the American Statistical Association 96, 185-193. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv32n1a07,
AUTHOR = {Gutiérrez, Hugo Andrés and Breidt, F. Jay},
TITLE = {{Estimation of the Population Total using the Generalized Difference Estimator and Wilcoxon Ranks}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2009},
volume = {32},
number = {1},
pages = {123-143}
}