Many statistics used to test that a sample of n points in the unit interval [0,1] comes from a known distribution can be studied using the theory of degenerate U- and V-statistics. In this theory, a special role is played by the eigenvalues of an integral operator. The aim of the present paper is to compare several versions of the Wielandt-Nyström method for the approximation of the eigenvalues of this integral operator. We apply it to compute the eigenvalues of the Anderson-Darling statistic.
Comparison of quadrature rules for the Wielandt-Nyström method with statistical applications
SERI, RAFFAELLO;
2012-01-01
Abstract
Many statistics used to test that a sample of n points in the unit interval [0,1] comes from a known distribution can be studied using the theory of degenerate U- and V-statistics. In this theory, a special role is played by the eigenvalues of an integral operator. The aim of the present paper is to compare several versions of the Wielandt-Nyström method for the approximation of the eigenvalues of this integral operator. We apply it to compute the eigenvalues of the Anderson-Darling statistic.
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