A K-sample Homogeneity Test based on the Quantification of the p-p Plot

Jeroen Hinloopen, Rien Wagenvoort, Charles van Marrewijk

Research output: Working paperProfessional

Abstract

We propose a quantification of the p-p plot that assigns equal weight to all distances between the respective distributions: the surface between the p-p plot and the diagonal. This surface is labelled the Harmonic Weighted Mass (HWM) index. We introduce the diagonal-deviation (d-d) plot that allows the index to be computed exactly under all circumstances. For two balanced samples absent ties the finite sample distribution of the HWM index is derived. Simulations show that in most cases unbalanced samples and ties have little effect on this distribution. The d-d plot allows for a straightforward extension to the K-sample HWM index. As we have not been able to derive the distribution of the index for K>2, we simulate significance tables for K=3,...,15. An example involving economic growth rates of the G7 countries illustrates that the HWM test can have better power than alternative Empirical Distribution Function tests.
Original languageEnglish
Place of PublicationAmsterdam
PublisherTinbergen Instituut
Publication statusPublished - 2008

Publication series

NameDiscussion paper TI
No.08-100/1

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homogeneity
plots
harmonics
deviation
economics
distribution functions
simulation

Cite this

Hinloopen, J., Wagenvoort, R., & van Marrewijk, C. (2008). A K-sample Homogeneity Test based on the Quantification of the p-p Plot. (Discussion paper TI; No. 08-100/1). Amsterdam: Tinbergen Instituut.
Hinloopen, Jeroen ; Wagenvoort, Rien ; van Marrewijk, Charles. / A K-sample Homogeneity Test based on the Quantification of the p-p Plot. Amsterdam : Tinbergen Instituut, 2008. (Discussion paper TI; 08-100/1).
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Hinloopen, J, Wagenvoort, R & van Marrewijk, C 2008 'A K-sample Homogeneity Test based on the Quantification of the p-p Plot' Discussion paper TI, no. 08-100/1, Tinbergen Instituut, Amsterdam.

A K-sample Homogeneity Test based on the Quantification of the p-p Plot. / Hinloopen, Jeroen; Wagenvoort, Rien; van Marrewijk, Charles.

Amsterdam : Tinbergen Instituut, 2008. (Discussion paper TI; No. 08-100/1).

Research output: Working paperProfessional

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T1 - A K-sample Homogeneity Test based on the Quantification of the p-p Plot

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AU - van Marrewijk, Charles

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N2 - We propose a quantification of the p-p plot that assigns equal weight to all distances between the respective distributions: the surface between the p-p plot and the diagonal. This surface is labelled the Harmonic Weighted Mass (HWM) index. We introduce the diagonal-deviation (d-d) plot that allows the index to be computed exactly under all circumstances. For two balanced samples absent ties the finite sample distribution of the HWM index is derived. Simulations show that in most cases unbalanced samples and ties have little effect on this distribution. The d-d plot allows for a straightforward extension to the K-sample HWM index. As we have not been able to derive the distribution of the index for K>2, we simulate significance tables for K=3,...,15. An example involving economic growth rates of the G7 countries illustrates that the HWM test can have better power than alternative Empirical Distribution Function tests.

AB - We propose a quantification of the p-p plot that assigns equal weight to all distances between the respective distributions: the surface between the p-p plot and the diagonal. This surface is labelled the Harmonic Weighted Mass (HWM) index. We introduce the diagonal-deviation (d-d) plot that allows the index to be computed exactly under all circumstances. For two balanced samples absent ties the finite sample distribution of the HWM index is derived. Simulations show that in most cases unbalanced samples and ties have little effect on this distribution. The d-d plot allows for a straightforward extension to the K-sample HWM index. As we have not been able to derive the distribution of the index for K>2, we simulate significance tables for K=3,...,15. An example involving economic growth rates of the G7 countries illustrates that the HWM test can have better power than alternative Empirical Distribution Function tests.

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Hinloopen J, Wagenvoort R, van Marrewijk C. A K-sample Homogeneity Test based on the Quantification of the p-p Plot. Amsterdam: Tinbergen Instituut. 2008. (Discussion paper TI; 08-100/1).