The Annals of Statistics

Large Sample Discrimination Between Two Gaussian Processes with Different Spectra

Ulf Grenander

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Abstract

We study the probability of error asymptotically for testing one Gaussian stochastic process against another when the mean vectors are zero and we have the choice between two given covariance matrices. It is shown that under certain conditions the probabilities of error form asymptotically a geometric progression with a ratio that is derived. The approach employs Laplace's method of approximating integrals and does not appeal to Fourier analysis; in this sense it can be said to be elementary.

Article information

Source
Ann. Statist., Volume 2, Number 2 (1974), 347-352.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342668

Digital Object Identifier
doi:10.1214/aos/1176342668

Mathematical Reviews number (MathSciNet)
MR356411

Zentralblatt MATH identifier
0277.62072

JSTOR
links.jstor.org

Subjects
Primary: 62M99: None of the above, but in this section

Keywords
Pattern discrimination error probability stationary processes

Citation

Grenander, Ulf. Large Sample Discrimination Between Two Gaussian Processes with Different Spectra. Ann. Statist. 2 (1974), no. 2, 347--352. doi:10.1214/aos/1176342668. https://projecteuclid.org/euclid.aos/1176342668


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