1Universidad Simón Bolívar, Departamento de Matemáticas Puras y Aplicadas, Caracas, Venezuela. Professor. Email: fojeda@usb.ve
2Universidad Simón Bolívar, Departamento de Cómputo Científico y Estadística, Caracas, Venezuela. Professor. Email: rosalvaph@gmail.com
3Universidad Simón Bolívar, Departamento de Cómputo Científico y Estadística, Caracas, Venezuela. Universidad de Los Andes, Departamento de Matemáticas, Bogotá, Colombia. Professor. Email: aj.quiroz1079@uniandes.edu.co ]]>
We present a non-parametric statistic based on a linearity measure of the P-P plot for the two-sample problem by adapting a known statistic proposed for goodness of fit to a univariate parametric family. A Monte Carlo comparison is carried out to compare the method proposed with the classical Wilcoxon and Ansari-Bradley statistics and the Kolmogorov-Smirnov and Cramér-von Mises statistics the two-sample problem, showing that, for certain relevant alternatives, the proposed method offers advantages, in terms of power, over its classical counterparts. Theoretically, the consistency of the statistic proposed is studied and a Central Limit Theorem is established for its distribution.
Key words: Nonparametric statistics, P-P plot, Two-sample problem.
Se presenta un estadístico no-paramétrico para el problema de dos muestras, basado en una medida de linealidad del gráfico P-P. El estadístico propuesto es la adaptación de una idea bien conocida en la literatura en el contexto de bondad de ajuste a una familia paramétrica. Se lleva a cabo una comparación Monte Carlo con los métodos clásicos de Wilcoxon y Ansari-Bradley, Kolmogorov-Smirnov y Cramér-von Mises para el probelam de dos muestras. Dicha comparación demuestra que el método propuesto ofrece una potencia superior frente a ciertas alternativas relevantes. Desde el punto de vista teórico, se estudia la consistencia del método propuesto y se establece un Teorema del Límite Central para su distribución.
Palabras clave: estadái sticos no-paramétricos, gráfico P-P, problema de dos muestras.
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv35n1a01,
AUTHOR = {Ojeda, Francisco M. and Pulido, Rosalva L. and Quiroz, Adolfo J. and Ríos, Alfredo J.}, ]]>
TITLE = {{Linearity Measures of the P-P Plot in the Two-Sample Problem}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2012},
volume = {35},
number = {1},
pages = {1-14}
}