TY - JOUR

T1 - On Uniform Consistency of Nonparametric Tests. I

AU - Ermakov, M.

PY - 2021/11/1

Y1 - 2021/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85117187936&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05582-1

DO - 10.1007/s10958-021-05582-1

M3 - Article

AN - SCOPUS:85117187936

VL - 258

SP - 802

EP - 837

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -