Details
| Original language | English |
|---|---|
| Pages (from-to) | 437 - 465 |
| Number of pages | 29 |
| Journal | Metrika |
| Volume | 83 |
| Issue number | 4 |
| Early online date | 3 Sept 2019 |
| Publication status | Published - May 2020 |
Abstract
We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
Keywords
- Crámer–von-Mises distance, Incomplete data, Marginal homogeneity test, Paired sample, Resampling test
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Metrika, Vol. 83, No. 4, 05.2020, p. 437 - 465.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data
AU - Gaigall, Daniel
PY - 2020/5
Y1 - 2020/5
N2 - We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
AB - We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
KW - Crámer–von-Mises distance
KW - Incomplete data
KW - Marginal homogeneity test
KW - Paired sample
KW - Resampling test
UR - http://www.scopus.com/inward/record.url?scp=85072110453&partnerID=8YFLogxK
U2 - 10.1007/s00184-019-00742-5
DO - 10.1007/s00184-019-00742-5
M3 - Article
VL - 83
SP - 437
EP - 465
JO - Metrika
JF - Metrika
SN - 0026-1335
IS - 4
ER -