Research Article Open Access

On the Probability Density Function of the Test Statistic for One Nonlinear GLR Detector Arising from fMRI

Fangyuan Nan

Abstract

Recently an important and interesting nonlinear generalized likelihood ratio (GLR) detector emerged in functional magnetic resonance imaging (fMRI) data processing. However, the study of that detector is incomplete: the probability density function (pdf) of the test statistic was draw from numerical simulations without much theoretical support and is therefore, not firmly grounded. This correspondence presents more accurate (asymptotic) closed form of the pdf by resorting to a non-central Wishart matrix and by asymptotic expansion of some integrals. It is then confirmed theoretically that the detector does possess constant false alarm rate (CFAR) property under some practical regimes of signal to noise ratio (SNR) for finite samples and the correct threshold selection method is given, which is very important for real fMRI data processing.

Journal of Mathematics and Statistics
Volume 3 No. 2, 2007, 38-43

DOI: https://doi.org/10.3844/jmssp.2007.38.43

Submitted On: 11 January 2007 Published On: 30 June 2007

How to Cite: Nan, F. (2007). On the Probability Density Function of the Test Statistic for One Nonlinear GLR Detector Arising from fMRI . Journal of Mathematics and Statistics, 3(2), 38-43. https://doi.org/10.3844/jmssp.2007.38.43

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Keywords

  • Generalized likelihood ratio test
  • non-central Wishart matrix
  • eigenvalue
  • probability density function
  • asymptotic analysis
  • asymptotic expansion
  • fMRI