Details
| Original language | English |
|---|---|
| Pages (from-to) | 300 - 327 |
| Number of pages | 28 |
| Journal | Statistics |
| Volume | 57 |
| Issue number | 2 |
| Publication status | Published - 2023 |
| Externally published | Yes |
Abstract
We consider Kolmogorov–Smirnov and Cramér–von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application.
Keywords
- 62G09, 62G10, Central symmetry test, exchangeability test, independence test, not identically distributed, random effects
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Statistics, Vol. 57, No. 2, 2023, p. 300 - 327.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the applicability of several tests to models with not identically distributed random effects
AU - Gaigall, Daniel
N1 - Publisher Copyright: © 2023 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2023
Y1 - 2023
N2 - We consider Kolmogorov–Smirnov and Cramér–von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application.
AB - We consider Kolmogorov–Smirnov and Cramér–von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application.
KW - 62G09
KW - 62G10
KW - Central symmetry test
KW - exchangeability test
KW - independence test
KW - not identically distributed
KW - random effects
UR - http://www.scopus.com/inward/record.url?scp=85150743298&partnerID=8YFLogxK
U2 - 10.1080/02331888.2023.2193748
DO - 10.1080/02331888.2023.2193748
M3 - Article
VL - 57
SP - 300
EP - 327
JO - Statistics
JF - Statistics
SN - 0323-3944
IS - 2
ER -