A K-Sample Homogeneity Test Based on the Quantification of the p-p Plot: The Harmonic Weighted Mass Index

Abstract

General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. September 2008AbstractWe 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 diagonaldeviation (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 * Thanks are due to Jan Kiviet, Robert Waldmann, Sanne Zwart, and seminar participants at the University of Adelaide, the University of Amsterdam, the University of Cyprus, and the Erasmus University Rotterdam for useful comments and constructive suggestions. The usual disclaimer applies.

Infrastructure Finance in Europe: Composition, Evolution and Crisis Impact

“…Hinloopen et al 2008). Differences that are significant at the 10-percent level are indicated with an asterisk.…”

“…Differences that are significant at the 10-percent level are indicated with an asterisk. Hinloopen et al 2008). Differences that are significant at the 10-percent level are indicated with an asterisk.…”

“…Conversely, the share of non-PPP project finance is significantly higher in the utility sector (16.4 percent) than in the transport sector (1.1 percent). Hinloopen et al 2008). Differences that are significant at the 10-percent level are indicated with an asterisk.…”

“…As regards the statistical methodology adopted in this article, the recently developed Harmonic Weighted Mass (HWM) index test (Hinloopen et al 2008) is applied in order to determine whether differences across categories, such as groups of countries or type of projects, are statistically significant. The HWM test is briefly explained in Box 1.…”

“…If, in contrast, OMS and NMS had identical investment shares, then the two cumulative distribution functions would be the same, and the p-p plot would coincide with the diagonal. Hinloopen et al (2008) therefore propose the area between the diagonal and the p-p plot for hypothesis testing. The associated Harmonic Weighted Mass (HWM) index test has several advantages over other EDF tests.…”