On the applicability of several tests to models with not identically distributed random effects. Issue 2 (4th March 2023)

• Record Type: Journal Article
• Authors: Gaigall, Daniel
• Is Part Of: Statistics. Volume 57:Issue 2(2023)
• Page Start: 300
• Page End: 327
• Publication Date: 2023-03-04
• Subjects: Central symmetry test -- exchangeability test -- independence test -- random effects -- not identically distributed; 62G10 -- 62G09; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2023.2193748
• Languages: English
• ISSNs: 0233-1888

Abstract

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.