Nonparametric integral statistics \(\omega_n^k=n^{k/2}\int_{-\infty}^\infty [S_n(x)-F(x)]^k dF(x)\): Main properties and applications (Q1382316)

In solving problems of experimental data processing in intermediate and high energy physics use is often made of nonparametric goodness-of-fit criteria based on the well-known \(\omega^2_n\) and \(\omega^3_n\) statistics. The present paper is devoted to a generalization of the properties of integral statistics \(\omega^k_n\), to an investigation of their distribution functions, to the construction of goodness-of-fit criteria, and to their comparison with known criteria of the type considered. A method for multidimensional data analysis based on \(\omega^k_n\)-criteria is described.