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

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  • Neuhaus, Georg

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.

Suggested Citation

  • Neuhaus, Georg, 1980. "A note on computing the distribution of the norm of Hilbert space valued Gaussian random variables," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 19-25, March.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:1:p:19-25
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    Cited by:

    1. Graciela Boente & Daniela Rodriguez & Mariela Sued, 2018. "Testing equality between several populations covariance operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 919-950, August.

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