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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.42 no.2 Bogotá July/Dec. 2019 

Artículos originales de investigación

Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions

Prueba simultánea de ubicación y parámetros de escala de dos distribuciones multivariables

Atul Chavana  , Digambar Shirkeb 

aDepartment of Statistics, Shivaji University, Kolhapur, India. E-mail:

bDepartment of Statistics, Shivaji University, Kolhapur, India. E-mail:


In this article, we propose nonparametric tests for simultaneously testing equality of location and scale parameters of two multivariate distributions by using nonparametric combination theory. our approach is to combine the data depth based location and scale tests using combining function to construct a new data depth based test for testing both location and scale parameters. Based on this approach, we have proposed several tests. Fisher’s permutation principle is used to obtain p-values of the proposed tests. Performance of proposed tests have been evaluated in terms of empirical power for symmetric and skewed multivariate distributions and compared to the existing test based on data depth. The proposed tests are also applied to a real-life data set for illustrative purpose.

Key words: Combining function; Data depth; Permutation test; Two-sample test


En este artículo, proponemos pruebas no paramétricas para probar simultáneamente la igualdad de ubicación y los parámetros de escala de dos distribuciones multivariantes mediante la teoría de combinaciones no paramétricas. Nuestro enfoque es combinar las pruebas de escala y ubicación basadas en la profundidad de los datos utilizando la función de combinación para construir una nueva prueba basada en la profundidad de los datos para probar los parámetros de ubicación y escala. Con base en este enfoque, hemos propuesto varias pruebas. El principio de permutación de Fisher se usa para obtener valores p de las pruebas propuestas. El rendimiento de las pruebas propuestas se ha evaluado en términos de potencia empírica para distribuciones multivariadas simétricas y asimétricas y se comparó con la prueba existente basada en la profundidad de los datos. Las pruebas propuestas también se aplican a un conjunto de datos de la vida real con fines ilustrativos.

Palabras-clave: Función de combinación; Profundidad de datos; Prueba de permutación; Prueba de dos muestras

Full text available only in PDF format.


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