TY  - JOUR
A1  - Gaigall, Daniel
T1  - On a new approach to the multi-sample goodness-of-fit problem
T2  - Communications in Statistics - Simulation and Computation
N2  - Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.
KW  - Goodness-of-fit test
KW  - Multi-sample problem
KW  - Parametric bootstrap
Y1  - 2019
UR  - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/10413
SN  - 1532-4141
VL  - 53
IS  - 10
SP  - 2971
EP  - 2989
PB  - Taylor & Francis
CY  - London
ER  -