TY  - JOUR
SP  - 1210
VL  - 27
JF  - Annals of Statistics
EP  - 1229
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/20895/
SN  - 0090-5364
TI  - Concentration and Goodness-of-Fit in Higher Dimensions: (Asymptotically) Distribution-Free Methods
KW  - Diagnostic plots; empirical process theory; generalized quantile transformation; Kolmogoroff-Smirnov test; minimum volume sets
N2  - A novel approach for constructing goodness-of-fit techniquesin arbitrary (finite) dimensions is presented. Testing problems are considered as well as the construction of diagnostic plots. The approach is based on some new notion of massconcentration, and in fact, our basic testing problems are fomulatedas problems for " 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 single hypotheses they are asymptotically distribution free with well known asymptotic distribution. The simple technical idea behind the approach may be called a generalizedquantile transformation, where the role of one-dimensional quantiles in classicalsituations is taken over by so-called minimum volume sets.
IS  - 4
Y1  - 1999///
PB  - IMS Business Office
AV  - public
A1  - Polonik, Wolfgang
CY  - Haward, Calif.
ID  - heidok20895
ER  -