Note on distribution free testing for discrete distributions
关于离散分布无分布检验的注记
The paper proposes one-to-one transformation of the vector of components $\{Y_{in}\}_{i=1}^{m}$ of Pearson’s chi-square statistic, \[Y_{in}=\frac{\nu_{in}-np_{i}}{\sqrt{np_{i}}},\qquad i=1,\ldots,m,\] into another vector $\{Z_{in}\}_{i=1}^{m}$, which, therefore, contains the same “statistical information,” but is asymptotically distribution free. Hence any functional/test statistic based on $\{Z_{in}\}_{i=1}^{m}$ is also asymptotically distribution free. Natural examples of…