Nonparametric Validation of Similar Distributions and Assessment of Goodness of Fit

Abstract

In this paper the problem of assessing the similarity of two cumulative distribution functions F and G is considered. An asymptotic test based on an -trimmed version of Mallows distance À F , G between F and G is suggested, thus demonstrating the similarity of F and G within a preassigned À F , G neighbourhood at a controlled type I error rate. The test proposed is applied to the validation of goodness of ®t and for the nonparametric assessment of bioequivalence. It is shown that À F , G can be interpreted as average and population equivalence. Our approach is illustrated by various examples.

On Hadamard differentiability in k-sample semiparametric models?with applications to the assessment of structural relationships

“…at the plot of the resulting p-values in dependence on the value of ∆ 0 (cf. [35]), which can serve as a valuable diagnostic tool in model checking and in comparing different models.…”

“…This choice of ∆ has some practical appeal [35] and is related to the Wasserstein distance between probability distributions. In the context of goodness-of-fit testing for parametric models in the one sample case, see [16,15] and the references given there.…”

Assessing the similarity of distributions - finite sample performance of the empirical mallows distance

“…In many applications we are interested in showing that two independent samples arise from similar underlying populations F and G. As pointed out by Munk & Czado (1995) testing the hypothesis H 0 : F = G versus K 0 : F 6 = G is not suitable for the assessment of similarity of populations, although this is common practice. Even when the observed p-value of a test for H 0 is large, this does not allow for a controlled error rate when assessing similarity.…”

“…Even when the observed p-value of a test for H 0 is large, this does not allow for a controlled error rate when assessing similarity. Therefore, Munk & Czado (1995) suggested interval hypotheses tests of the form H : (F; G) > 0 versus K : (F; G) 0 ;…”

“…'s) has been the topic of a previous paper by the authors (Munk & Czado (1995)). Here, we developed an asymptotic test based on a trimmed version of the Mallows distance (Mallows 1972) between two c.d.f.…”