论文标题
在非参数测试的一致性上
On uniform consistency of nonparametric tests I
论文作者
论文摘要
我们指出，对于广泛的非参数测试，非参数替代方案的一致性均匀的必要条件。可以根据分布函数和密度（或高斯白噪声中信号检测问题的信号）来定义非参数替代方案集。在本文的这一部分中，为$χ^2- $测试提供了这种条件，随着细胞数量的增加，Cramer-von Mises测试，生成$ \ MATHBB {l} _2 $ - 内核估计器的规范和测试生成的二次估算值的估算值的测试。
We point out necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives for widespread nonparametric tests. Nonparametric sets of alternatives can be defined both in terms of distribution function and in terms of density (or signals in the problem of signal detection in Gaussian white noise). In this part of paper such conditions are provided for $χ^2-$tests with increasing number of cells, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients.
