For widespread nonparametric tests, we point out necessary and sufficient conditions of uniform consistency for nonparametric sets of alternatives. Nonparametric sets of alternatives can be defined both in terms of distribution functions and in terms of density. Such conditions are provided for χ2-tests with an increasing number of cells, for Cramér – von Mises tests, for tests generated by L2-norms of kernel estimators, and for tests generated by quadratic forms of estimators of Fourier coefficients. Necessary and sufficient conditions on sets of alternatives for the existence of uniformly consistent tests are treated as well.
Original languageEnglish
Pages (from-to)802-837
Number of pages36
JournalJournal of Mathematical Sciences (United States)
Volume258
Issue number6
DOIs
StatePublished - 1 Nov 2021

ID: 129368320