A Cramér–von Mises Test for Gaussian Processes

Gennady Martynov ()
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Gennady Martynov: Kharkevich Institute for Information Transmission Problems

A chapter in Mathematical Statistics and Limit Theorems, 2015, pp 209-229 from Springer

Abstract: 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.

Keywords: Goodness-of-fit test; Cramér–von Mises test; Gaussianity test; Hilbert space (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-12442-1_12

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DOI: 10.1007/978-3-319-12442-1_12

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