Title: On maxispaces of nonparametric tests,
Abstract: For the problems of nonparametric hypothesis testing we introduce the notion
of maxisets and maxispace. We point out the maxisets of $\chi^2-$tests,
Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel
estimators and tests generated quadratic forms of estimators of Fourier
coefficients. For these tests we show that, if sequence of alternatives having
given rates of convergence to hypothesis is consistent, then each altehrnative
can be broken down into the sum of two parts: a function belonging to maxiset
and orthogonal function. Sequence of functions belonging to maxiset is
consistent sequence of alternatives.
We point out asymptotically minimax tests if sets of alternatives are maxiset
with deleted "small" $\mathbb{L}_2$-balls.