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A Cramér–von Mises Test for Gaussian Processes

In: Mathematical Statistics and Limit Theorems

Author

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  • Gennady Martynov

    (Kharkevich Institute for Information Transmission Problems
    Higher School of Economics)

Abstract

We propose a statistical method for testing the null hypothesis that an observed random process on the interval $$[0,1]$$ [ 0 , 1 ] is a mean zero Gaussian process with specified covariance function. Our method is based on a finite number of observations of the process. To test this null hypothesis, we develop a Cramér–von Mises test based on an infinite-dimensional analogue of the empirical process. We also provide a method for computing the critical values of our test statistic. The same theory also applies to the problem of testing multivariate uniformity over a high-dimensional hypercube. This investigation is based upon previous joint work by Paul Deheuvels and the author.

Suggested Citation

  • Gennady Martynov, 2015. "A Cramér–von Mises Test for Gaussian Processes," Springer Books, in: Marc Hallin & David M. Mason & Dietmar Pfeifer & Josef G. Steinebach (ed.), Mathematical Statistics and Limit Theorems, edition 127, pages 209-229, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12442-1_12
    DOI: 10.1007/978-3-319-12442-1_12
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