p-p plots and precedence tests for planar point processes
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TLDR
In this article, the authors extended the notion of precedence test to higher dimensions and found two different tests that are appropriate for both partial and complete data sets, based on two different extensions of the usual definition of a procentile-procentile plot.Abstract:
Let Xi,X2,. • • ,Xn be a random sample of size n from a continuous distribution F and Y1}Y2,..., Ym be a random sample of size m from a continuous distribution G. One of the ways to test the hypothesis of equality of F and G against the alternative that F < G when both distributions are univariate is to perform a precedence test -a test that not only requires only a portion of the samples, but which is distribution-free under the null hypothesis. The initial purpose of this thesis was to extend the notion of a precedence test to higher dimensions. In doing so, we found two different tests that are appropriate for both partial and complete data sets. These tests are based on two different extensions of the usual definition of a procentile-procentile plot -which is closely related to the precedence test statistic on the lineto the plane. The first of the above mentioned extensions involves the contours formed by the distribution function F; the second of our tests uses the marginal quantiles of F. For both extensions of the empirical p — p plot, we have proven a Glivenko-Cantelli type of result. Also, we have developed their asymptotic convergence to Gaussian limits. The choice between tests based on these two plots depends on the kind of information that the data of our experiment generates. All the results presented here, although mostly presented for !ft, are valid for 3?-valued data.read more
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Journal ArticleDOI
Multidimensional p-p plots and precedence tests for point processes on R d
Adriana Jordan,B. Gail Ivanoff +1 more
TL;DR: Given two univariate distributions F and G, the hypothesis that F=G can be tested against the alternative that F is different from G.
Journal ArticleDOI
One-dimensional p-p plots and precedence tests for point processes on ℝ d
A. Jordan,B. G. Ivanoff +1 more
TL;DR: In this article, a generalization of the precedence test and the corresponding p-p plot is proposed for a test of F = G against the alternative that F ≺ G for various stochastic orders on Ω(n, d).
References
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Weak convergence of empirical copula processes
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