Abstract
We propose a statistical method for testing the null hypothesis that an observed random process on the interval \([0,1]\) 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.
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Acknowledgments
The author would like to express his appreciation and thanks to Professor Paul Deheuvels for their long cooperation. The author is also grateful to the editors of this Festschrift for their constructive comments.
The work was partly supported by the Russian Foundation for Basic Research (RFBR), grant N 13-01-12447.
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Martynov, G. (2015). A Cramér–von Mises Test for Gaussian Processes. In: Hallin, M., Mason, D., Pfeifer, D., Steinebach, J. (eds) Mathematical Statistics and Limit Theorems. Springer, Cham. https://doi.org/10.1007/978-3-319-12442-1_12
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DOI: https://doi.org/10.1007/978-3-319-12442-1_12
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