@article{Gaigall2023,
  author    = {Gaigall, Daniel},
  title     = {On the applicability of several tests to models with not identically distributed random effects},
  series = {Statistics : A Journal of Theoretical and Applied Statistics},
  volume    = {57},
  journal   = {Statistics : A Journal of Theoretical and Applied Statistics},
  publisher = {Taylor \& Francis},
  address   = {London},
  isbn      = {0323-3944},
  issn      = {1029-4910},
  doi       = {10.1080/02331888.2023.2193748},
  pages     = {14 Seiten},
  year      = {2023},
  abstract  = {We consider Kolmogorov-Smirnov and Cram{\´e}r-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.},
  language  = {en}
}
@article{Gaigall2020,
  author    = {Gaigall, Daniel},
  title     = {Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic on partly not identically distributed data},
  series = {Communications in Statistics - Theory and Methods},
  volume    = {51},
  journal   = {Communications in Statistics - Theory and Methods},
  number    = {12},
  publisher = {Taylor \& Francis},
  address   = {London},
  issn      = {1532-415X},
  doi       = {10.1080/03610926.2020.1805767},
  pages     = {4006 -- 4028},
  year      = {2020},
  abstract  = {The established Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic is investigated for partly not identically distributed data. Surprisingly, it turns out that the statistic has the well-known distribution-free limiting null distribution of the classical criterion under standard regularity conditions. An application is testing goodness-of-fit for the regression function in a non parametric random effects meta-regression model, where the consistency is obtained as well. Simulations investigate size and power of the approach for small and moderate sample sizes. A real data example based on clinical trials illustrates how the test can be used in applications.},
  language  = {en}
}