On uniform consistency of Neyman’s type nonparametric tests

The goodness-of-fit problem is explored, when the test statistic a linear combination of squared Fourier coefficients’ estimates coming from decomposition probability density. Common examples such statistics include Neyman’s and statistics, generated by L2-norms kernel estimators. We prove asymptotic normality for both null alternative hypothesis. Using these results we deduce conditions uniform consistency nonparametric sets alternatives, which are defined in terms distribution or density functions. Results on consistency, related to functions, can be seen as statement showing what extent distance method, based given statistic, makes hypothesis alternatives distinguishable. In this case, deduced close necessary. For sequences - functions approaching L2-metric, find necessary sufficient their consistency. This result obtained concept maxisets, description found publication.