Nonparametric integral statistics w(n)(k)=n(k/2) integral(infinity)(-infinity)[S-n(x)-F(x)](k)dF(x): Main properties and applications
The main characteristics of nonparametric statistics, omega(n)(k), which can be represented as integrals of the k(th) degree of the empirical process, are considered. An algebraic form of these statistics, convenient for practical usage, is derived. Tables of percentage points for k = 1, 2,...,5 and small empirical sample sizes n = 1, 2,...,10 are obtained. Goodness-of-fit criteria based on omega(n)(k) statistics are constructed, and their main properties are studied. A method for classifying multidimensional data based on these criteria, which was successfully applied in several experiments, is described.
nonparametric statistics goodness-of-fit criteria multidimensional data analysis pattern recognition