HausdorffGoF - One- And Two-Sample Hausdorff Goodness-of-Fit Test
Computes the test statistic and p-values of the one-sample
and two-sample Hausdorff (H) goodness-of-fit tests. The H
statistic measures the Hausdorff distance under the Chebyshev
(l-infinity) metric, between the two cumulative distribution
functions (cdfs) underlying the corresponding one-sample and
two-sample null hypothesis. It coincides to the side length of
the largest axis-aligned square (hypercube) that can be
inscribed between the two cdfs. The following cases are
covered: (i) one-sample, univariate; (ii) two-sample
univariate; and (iii) two-sample bivariate. Exact one-sample
p-values are computed in O(n^2 log n) time via the
'Exact-KS-FFT' method of Dimitrova, Kaishev, and Tan (2020)
<doi:10.18637/jss.v095.i10>; two-sample p-values are obtained
by permutation. A key advantage of the H test is that its
sensitivity can be directed towards the left tail, body, or
right tail of the distribution by tuning a scale parameter
sigma, and therefore maximizing its power which as shown
numerically is significantly higher than the power of the
classical tests such as the Kolmogorov-Smirnov, Cramer-von
Mises, and Anderson-Darling test, especially when the right
tail of the distribution is targeted. The sensitivity of the
test (left tail, body, or right tail) is governed by two
parameters psi1 and psi2, whose values needs to be input. Then
the optimal value of the scale parameter sigma is automatically
computed.
