A novel approach for constructing goodness-of-fit techniques in
arbitrary finite dimensions is presented. Testing problems are considered as
well as the construction of diagnostic plots. The approach is based on some new
notions of mass concentration, and in fact, our basic testing problems are
formulated as problems of
‘‘goodness-of-concentration.’’ It is this
connection to concentration of measure that makes the approach conceptually
simple. The presented test statistics are continuous functionals of certain
processes which behave like the standard one-dimensional uniform empirical
process. Hence, the test statistics behave like classical test statistics for
goodness-of-fit. In particular, for simple hypotheses they are asymptotically
distribution free with well-known asymptotic distribution. The simple technical
idea behind the approach may be called a generalized quantile transformation,
where the role of one-dimensional quantiles in classical situations is taken
over by so-called minimum volume sets.
@article{1017938922,
author = {Polonik, Wolfgang},
title = {Concentration and goodness-of-fit in higher dimensions:
(asymptotically) distribution-free methods},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1210-1229},
language = {en},
url = {http://dml.mathdoc.fr/item/1017938922}
}
Polonik, Wolfgang. Concentration and goodness-of-fit in higher dimensions:
(asymptotically) distribution-free methods. Ann. Statist., Tome 27 (1999) no. 4, pp. 1210-1229. http://gdmltest.u-ga.fr/item/1017938922/