Details
| Original language | English |
|---|---|
| Pages (from-to) | 2971-2989 |
| Number of pages | 19 |
| Journal | Communications in Statistics Part B: Simulation and Computation |
| Volume | 50 |
| Issue number | 10 |
| Publication status | Published - 22 May 2019 |
Abstract
Suppose we have k samples X 1,1..,X 1,n1..,X k,1..,X k,nk with different sample sizes n 1,...,n k and unknown underlying distribution functions F 1,...,F k as observations plus k families of distribution functions (Formula presented.) each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not F 1,...,F k belongs to the parametric family (Formula presented.) 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.
Keywords
- Goodness-of-fit test, Multi-sample problem, Parametric bootstrap
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Modelling and Simulation
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In: Communications in Statistics Part B: Simulation and Computation, Vol. 50, No. 10, 22.05.2019, p. 2971-2989.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - On a new approach to the multi-sample goodness-of-fit problem
AU - Gaigall, Daniel
N1 - Publisher Copyright: © 2019, © 2019 Taylor & Francis Group, LLC.
PY - 2019/5/22
Y1 - 2019/5/22
N2 - Suppose we have k samples X 1,1..,X 1,n1..,X k,1..,X k,nk with different sample sizes n 1,...,n k and unknown underlying distribution functions F 1,...,F k as observations plus k families of distribution functions (Formula presented.) each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not F 1,...,F k belongs to the parametric family (Formula presented.) 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.
AB - Suppose we have k samples X 1,1..,X 1,n1..,X k,1..,X k,nk with different sample sizes n 1,...,n k and unknown underlying distribution functions F 1,...,F k as observations plus k families of distribution functions (Formula presented.) each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not F 1,...,F k belongs to the parametric family (Formula presented.) 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
UR - http://www.scopus.com/inward/record.url?scp=85066886364&partnerID=8YFLogxK
U2 - 10.1080/03610918.2019.1618472
DO - 10.1080/03610918.2019.1618472
M3 - Article
VL - 50
SP - 2971
EP - 2989
JO - Communications in Statistics Part B: Simulation and Computation
JF - Communications in Statistics Part B: Simulation and Computation
SN - 0361-0918
IS - 10
ER -