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ESTUDIO SOBRE LOS EFECTOS DEL PARÁMETRO DE SUAVIZADO EN CONTRASTES NO PARAMÉTRICOS PARA K–MUESTRAS
STUDYING THE BANDWIDTH EFFECTS IN NON PARAMETRIC K–SAMPLE TESTS
Keywords:
tests no paramétricos, estimación núcleo, parámetro ventana (es)Nonparametric tests, Kernel estimation, Bandwidth (en)
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1Subdirección de Salud Pública de Gipuzkoa, CIBER Epidemiología y Salud Pública, Donostia, España. Investigador postdoctoral. Email: pmcamblor@hotmail.com
Una de las principales limitaciones de las técnicas de suavizamiento es la necesidad de elegir un parámetro de suavizado o ventana. La influencia de este parámetro sobre los resultados obtenidos obliga a que el uso de estos métodos en inferencia sea delicado, ya que la decisión final puede verse determinada por la elección del parámetro. El objetivo principal de este trabajo es el estudio de algunos algoritmos para el cálculo automático del parámetro ventana en problemas de contrastes de hipótesis para la igualdad de k poblaciones independientes.
Palabras clave: tests no paramétricos, estimación núcleo, parámetro ventana.
The election of the smoothing parameter or bandwidth is, probably, the most important concern in the statistical smoothed techniques. The relevance of this parameter, on the obtained results difficult, the use of these methods in statistical inference, because the final decision could be determined for the used bandwidth. The main goal of this paper is discussing and studying some algorithms for the automatic computation of the bandwidth in k--sample problems.
Key words: Nonparametric tests, Kernel estimation, Bandwidth.
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Referencias
1. Ahmad, A. I. & Li, Q. (1997), `Testing Symmetry of an Unknown Density Function by Kernel Method´, Journal of Nonparametric Statistics 7, 279-293.
2. Anderson, N. H., Hall, P. & Titterington, D. M. (1994), `Two-Sample Test Statistics for Measuring Discrepancies between two Multivariate Probability Density Functions using Kernel-Based Density Estimates´, Journal of Multivariante Analysis 50, 41-54.
3. Bowman, A. & Azzalini, A. (2001), Applied Smoothing Techniques for Data Analysis, Oxford University Press, Oxford, United Kingdom.
4. Cao, R. (1990), Aplicaciones y nuevos resultados del método Bootstrap en la estimación no paramétrica de curvas, Tesis Doctoral, Universidad de Santiago de Compostela.
5. Cao, R. & Van Keilegom, I. (2006), `Empirical Likelihood Tests for Two-Sample Problems via Nonparametric Density Estimation´, Canad. J. Statist. 34, 61-77.
6. Devroye, L. & Györfy, L. (1985), Nonparametric Density Estimation: The L1\, View, John Wiley & Son, New York, United States.
7. Diks, D. & Tong, H. (1999), `A Test for Simmetries of Multivatiate Probability Distributions´, Biometrika 86(3), 605-614.
8. Eggermont, P. P. B. & LaRiccia, V. N. (2003), Selecting the Smoothing Parameter in Goodness of Fit Testing. Consultado el 04/06/08 en la web:. *www.udel.edu/FREC/eggermont/Preprints/smoselnew.pdf
9. Fan, Y. (1994), `Testing the Goodness of Fit of a Parametric Density Function by Kernel Method´, Econometric Theory 10, 316-356.
10. Fan, Y. (1998), `Goodness-of-fit Tests Based on Kernel Density Estimators with Fixed Smoothing Parameters´, Econometric Theory 14, 604-621.
11. Ghosh, B. K. & Huang, W. M. (1991), `The Power and Optimal Kernel of the Bickel-Rosenblatt Test for Goodness of Fit´, Annals of Statistics 19(2), 999-1008.
12. Hall, P., DiCiccio, J. T. & Romano, J. P. (1989), `On Smoothing and the Bootstrap´, Annals of Statistics 17(2), 692-704.
13. Hall, P. & York, M. (2001), `On the Calibration or Silverman's Test for Multimodality´, Statistica Sinica 11, 516-536.
14. Horvath, L. (1991), `On L_p-norms of Multivariate Density Estimations´, Annals of Statistics 19(4), 1933-1949.
15. Li, Q. (1996), `Nonparametric Testing of Closeness Between two Unknown Distributions Functions´, Econometric Review 15(3), 216-274.
16. Li, Q. (1999), `Nonparametric Testing the Similarity of two Unkown Density Functions: Local Power and Bootstrap Analysis´, Journal of Nonparametric Statistics 11, 189-213.
17. Liero, H., Läuter, H. & Konakov, V. (1998), `Nonparametric versus Parametric Goodness of Fit´, Statistics 31, 115-149.
18. Martínez-Camblor, P. (2006), Tests no paramétricos basados en una distancia entre funciones de densidad, Servicio de Publicaciones de la Universidad de Oviedo, Oviedo, España.
19. Martínez-Camblor, P. (2008), `Test de hipótesis para contrastar la igualdad entre k-poblaciones´, Revista Colombiana de Estadística 31(1), 1-18.
20. Martínez-Camblor, P. & Corral, N. (2008), `Weaker Conditions for Asymptotic Approximation to L_P-norms of the Kernel Estimators´, InterSTAT Journal june, 1-18.
21. Martínez-Camblor, P., De Uña, J. & Corral, N. (2008), `K-Sample Test Based on the Common Area of Kernel Density Estimator´, Journal of Statistical Planning and Inference 138(12), 4006-4020.
22. Martínez-Camblor, P. & De Uña-Álvarez, J. (2008), Nonparametric k-sample Tests: Density Function vs. Distribution Function, Discussion Papers in Statistics and Operation Research Report 08/09, Universidade de Vigo, Dpto. de Estadística e Investigación Operativa.
23. Nadaraya, E. A. (1964), `Some New Estimates for Distribution Functions´, Theory Prob. Applic. 9, 497-500.
24. Parzen, E. (1962), `On Estimation of a Probability Density Function and Mode´, Annals of Mathematical Statistics 33, 832-837.
25. Rosenblatt, M. (1956), `Remarks on Some Nonparametric Estimates of a Density Functions´, Ann. Math. Statistics 27, 832-837.
26. Sarda, P. (1993), `Smoothing Parameter Selection for Smooth Distribution Function´, Journal of Statistical Planning and Inference 35, 65-75.
27. Silverman, B. W. (1981), `Using Kernel Density Estimation to Investigate Multimodality´, Journal of the Royal Statistics Society B(43), 97-99.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv31n2a02,
AUTHOR = {Martínez-Camblor, Pablo},
TITLE = {{Estudio sobre los efectos del parámetro de suavizado en contrastes no paramétricos para k--muestras}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2008},
volume = {31},
number = {2},
pages = {157-168}
}
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