Estimation of the population total using the generalized difference estimator and Wilcoxon ranks

• HUGO ANDRÉS GUTIÉRREZ ^[1] ; F. JAY BREIDT ^[2]
  1. [1] Universidad Santo Tomás

     Universidad Santo Tomás

     Santiago, Chile

     
  2. [2] Colorado State University

     Colorado State University

     Estados Unidos

     
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 32, Nº. 1, 2009, págs. 123-143
• Idioma: inglés
• Títulos paralelos:
  • Estimación del total poblacional usando el estimador de diferencia generalizada y los rangos de Wilcoxon
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • Breidt, F. J.,Opsomer, J. D.. (2000). `Local Polynomial Regression Estimators in Survey Sampling´. The Annals of Statistics. 28. 1026-1053
  • Cassel, C. M.,Särndal, C. E.,Wretman, J.. (1976). `Some Results on Generalized Difference Estimation and Generalized Regression Estimation...
  • Cassel, C. M.,Särndal, C. E.,Wretman, J.. (1976). Foundations of Inference in Survey Sampling. Wiley. New York.
  • Chen, J.,Qin, J.. (1993). `Empirical Likelihood Estimation for Finite Populations and the Efectivene Usage of Auxiliary Information´....
  • Deville, J. C.,Särndal, C. E.. (1992). `Calibration Estimators in Survey Sampling´. Journal of the American Statistical Association. 87....
  • Draper, D.. (1988). `Rank-Based Robust Analysis of Linear Models I. Exposition and Review´. Statistical Science. 3. 239-257
  • Hettmansperger, T. P.. (1984). Statistical Inference Based on Ranks. Wiley. New York.
  • Hettmansperger, T. P.,McKean, J. W.. (1998). Robust Nonparametric Statistical Methods. Arnold.
  • Horvitz, D. G.,Thompson, D. J.. (1952). `A Generalization of Sampling Without Replacement from a Finite Universe´. Journal of the American...
  • Isaki, C. T.,Fuller, W. A.. (1982). `Survey Design under the Regression Superpopulation Model´. Journal of the American Statistical Association....
  • Jaeckel, L.. (1972). `Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals´. The Annals of Mathematical Statistics....
  • Jurecková, J.. (1971). `Nonparametric Estimate of Regression Coefficients´. The Annals of Mathematical Statistics. 42. 1328-1338
  • Lohr, S.. (1999). Sampling: Design and Analysis. Duxbury Press. California.
  • Särndal, C. E.. (1980). `On \pi-inverse Weighting Versus best Linear Unbiased Weighting in Probability Sampling´. Biometrika. 67. 639-650
  • Särndal, C. E.,Swensson, B.,Wretman, J.. (1989). `The Weighted Residual Technique for Estimating the Variance of the General Regression...
  • Särndal, C. E.,Swensson, B.,Wretman, J.. (1992). Model Assisted Survey Sampling. Springer. New York.
  • (2007). Team, R. D. C. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna.
  • Terpstra, J. F.,McKean, J. W.. (2005). `Rank-based analyses of linear models using R´. Journal of Statistical Software. 14. 1-26
  • Wu, C.. (2003). `Optimal Calibration Estimators in Survey Sampling´. Biometrika. 90. 937-951
  • Wu, C.,Sitter, R. R.. (2001). `A Model Calibration Approach to Using Complete Auxiliary Information from Survey Data´. Journal of the...