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Discrete approximation of integral operators. (English) Zbl 1119.47067
Summary: A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.

MSC:
47N30 Applications of operator theory in probability theory and statistics
47G10 Integral operators
47A75 Eigenvalue problems for linear operators
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
65R20 Numerical methods for integral equations
65J05 General theory of numerical analysis in abstract spaces
45C05 Eigenvalue problems for integral equations
45P05 Integral operators
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