A note on computing the distribution of the norm of Hilbert space valued Gaussian random variables

Georg Neuhaus

Journal of Multivariate Analysis, 1980, vol. 10, issue 1, 19-25

Abstract: Let X be a Gaussian rv with values in a separable Hilbert space H having a covariance operator R of the form R = L0*A*AL0, where L0, A are linear operators on H. A method is given for computing in terms of R0 = L0*L0 and A the distribution of X2, · being the norm in H. The result is applied to the evaluation of the asymptotic distribution of Cramér-von Mises statistics when parameters are present. L0 corresponds to the case where the true underlying parameter is known and A represents the effect of estimating the unknown parameter.

Keywords: Gaussian; process; Hilbert; space; distribution; of; the; norm; Cramer-von; Mises; statistic; estimated; parameters (search for similar items in EconPapers)
Date: 1980
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Citations: View citations in EconPapers (1)

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