Published

2019-07-01

Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions

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

DOI:

https://doi.org/10.15446/rce.v42n2.70815

Keywords:

Combining function, Data depth, Permutation test, Two-sample test (en)
Función de combinación, Profundidad de datos, Prueba de permutación, Prueba de dos muestras (es)

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Authors

  • Atul Rajaram Chavan Shivaji University - Department of Statistics
  • Digambar Tukaram Shirke Shivaji University - Department of Statistics
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 has 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.
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.

References

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How to Cite

APA

Chavan, A. R. and Shirke, D. T. (2019). Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions. Revista Colombiana de Estadística, 42(2), 185–208. https://doi.org/10.15446/rce.v42n2.70815

ACM

[1]
Chavan, A.R. and Shirke, D.T. 2019. Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions. Revista Colombiana de Estadística. 42, 2 (Jul. 2019), 185–208. DOI:https://doi.org/10.15446/rce.v42n2.70815.

ACS

(1)
Chavan, A. R.; Shirke, D. T. Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions. Rev. colomb. estad. 2019, 42, 185-208.

ABNT

CHAVAN, A. R.; SHIRKE, D. T. Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions. Revista Colombiana de Estadística, [S. l.], v. 42, n. 2, p. 185–208, 2019. DOI: 10.15446/rce.v42n2.70815. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/70815. Acesso em: 28 mar. 2025.

Chicago

Chavan, Atul Rajaram, and Digambar Tukaram Shirke. 2019. “Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions”. Revista Colombiana De Estadística 42 (2):185-208. https://doi.org/10.15446/rce.v42n2.70815.

Harvard

Chavan, A. R. and Shirke, D. T. (2019) “Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions”, Revista Colombiana de Estadística, 42(2), pp. 185–208. doi: 10.15446/rce.v42n2.70815.

IEEE

[1]
A. R. Chavan and D. T. Shirke, “Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions”, Rev. colomb. estad., vol. 42, no. 2, pp. 185–208, Jul. 2019.

MLA

Chavan, A. R., and D. T. Shirke. “Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions”. Revista Colombiana de Estadística, vol. 42, no. 2, July 2019, pp. 185-08, doi:10.15446/rce.v42n2.70815.

Turabian

Chavan, Atul Rajaram, and Digambar Tukaram Shirke. “Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions”. Revista Colombiana de Estadística 42, no. 2 (July 1, 2019): 185–208. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/70815.

Vancouver

1.
Chavan AR, Shirke DT. Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions. Rev. colomb. estad. [Internet]. 2019 Jul. 1 [cited 2025 Mar. 28];42(2):185-208. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/70815

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CrossRef citations2

1. Atul R Chavan, Digambar T Shirke. (2020). Nonparametric two sample tests for scale parameters of multivariate distributions. Communications for Statistical Applications and Methods, 27(4), p.397. https://doi.org/10.29220/CSAM.2020.27.4.397.

2. Rosa Arboretti, Elena Barzizza, Nicoló Biasetton, Marta Disegna. (2025). A review of multivariate permutation tests: Findings and trends. Journal of Multivariate Analysis, 207, p.105421. https://doi.org/10.1016/j.jmva.2025.105421.

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