Published

2010-07-01

FUNCIONES DE VARIANZA Y CORRELACIÓN BICUADRÁTICA PARA DISTRIBUCIONES NORMALES

BIWEIGHT VARIANCE AND CORRELATION FUNCTIONS FOR NORMAL DISTRIBUTIONS

Keywords:

coeficiente de correlación, distribución truncada, estimación robusta, estimador M (es)
Correlation coefficient, M-estimate, Truncated distribution, Robust estimation (en)

Downloads

Authors

  • Carlos Eduardo Alonso Universidad Nacional de Colombia
  • Jorge Martínez Universidad Nacional de Colombia
En este trabajo se analiza el comportamiento del funciona ϱ asociado al estimador de correlación bicuadrático – ϱ̂ –, asumiendo que se observan vectores aleatorios con distribución normal bivariada. Esto, con el objetivo de verificar si este estimador robusto es un estimador insesgado del coeficiente de correlación –ρ–. El trabajo se desarrolló a partir de las propiedades de la función generadora de momentos de una distribución. De acuerdo con los resultados, ϱ > ρ cuando ρ < 0, ϱ < ρ cuando ρ > 0, y ϱ = 0 cuando ρ = 0, e indican que el estimador propuesto ϱ̂ no es un estimador insesgado del coeficiente de correlación. Lo anterior plantea como reto modificar el estimador ϱ̂ con el objetivo de obtener un estimador robusto insesgado o asintóticamente insesgado del coeficiente de correlación.
In this paper, we have analized the behavior of the functional ϱ, associated to the bi weight correlation estimator – ϱ̂ –, assuming the sampled population has a bivariate normal distribution. The purpose is to verify if the estimator ϱ̂ is an unbiased estimator of the correlation coefficient ρ. The results show ϱ > ρ when ρ < 0, ϱ < ρ when ρ > 0, y ϱ= 0 when ρ = 0. This results indicate ϱ̂ is not an unbiased estimator of the correlation coefficient.

Downloads

Download data is not yet available.

References

Beaton, A. & Tukey, J. (1974), The Fitting of Power Series, Meaning

Polynomials, Illustrated on Band-Spectroscopic Data', Technometrics 16

(2), 147-185.

Bickel, P. & Docksum, K. (1977), Mathematical Statistics, Basic Ideas and Selected Topics, Holden-day Inc., San Rancisco.

Cohen, C. (1955), 'Restriction and Selection in Samples from Bivariate Normal Distributions', Journal of the American Statistical Association 50(271), 884-893.

Finney, D. (1962), `Cumulants of Truncated Multi-Normal Distributions',

Journal of the Royal Statistical Society, serie B 24(2), 535-536.

Khatri, C. & Jaiswal, M. (1963), 'Estimation of Parameters of a Truncated Bivariate Normal Distribution', Journal of the American Statistical

Association 58(302), 519-526.

Lax, D. (1975), An Interim Report of a Monte Carlo Study of Robust Estimators of Widthers, Technical report, Department of Statistics, Princeton University.

Rosenbaum, S. (1961), 'Moments of a Truncated Bivariate Normal Distribution', Journal of the Royal Statistical Society 23(2), 405-408.

Singh, N. (1960), 'Estimation of Parameters of a Multivariate Normal Popula-tion from Truncated and Censured Samples', Journal of the Royal Statistical Society, serie B 22 (2), 307-311.

Tallis, G. (1961), 'The Moment Generating Function of the Truncated Multinormal Distribution', Journal of the Royal Statistical Society, serie B 23(1), 223-229.

Valcarcel, H. (2007), Propuesta de una funciOn de autocorrelación con base en la función bicuadrática, Trabajo de grado, Departamento de Estadistica, Universidad Nacional de Colombia, Bogota.

Wei, W. (2006), Time Series Analysis: Univariate and Multivariate

Methods, second edn, Addison Wesley, Boston.

License

Copyright (c) 2010 Revista Colombiana de Estadística

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).