A note on computing the distribution of the norm of Hilbert space valued Gaussian random variables
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.
Year of publication: |
1980
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Authors: | Neuhaus, Georg |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 10.1980, 1, p. 19-25
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Publisher: |
Elsevier |
Keywords: | Gaussian process Hilbert space distribution of the norm Cramer-von Mises statistic estimated parameters |
Saved in:
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