The Annals of Statistics

Semiparametric detection of significant activation for brain fMRI

Chunming Zhang and Tao Yu

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Functional magnetic resonance imaging (fMRI) aims to locate activated regions in human brains when specific tasks are performed. The conventional tool for analyzing fMRI data applies some variant of the linear model, which is restrictive in modeling assumptions. To yield more accurate prediction of the time-course behavior of neuronal responses, the semiparametric inference for the underlying hemodynamic response function is developed to identify significantly activated voxels. Under mild regularity conditions, we demonstrate that a class of the proposed semiparametric test statistics, based on the local linear estimation technique, follow χ2 distributions under null hypotheses for a number of useful hypotheses. Furthermore, the asymptotic power functions of the constructed tests are derived under the fixed and contiguous alternatives. Simulation evaluations and real fMRI data application suggest that the semiparametric inference procedure provides more efficient detection of activated brain areas than the popular imaging analysis tools AFNI and FSL.

Article information

Ann. Statist., Volume 36, Number 4 (2008), 1693-1725.

First available in Project Euclid: 16 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62G10: Hypothesis testing
Secondary: 62F30: Inference under constraints 65F50: Sparse matrices

deconvolution local polynomial regression nonparametric test spatio-temporal data stimuli time resolution


Zhang, Chunming; Yu, Tao. Semiparametric detection of significant activation for brain fMRI. Ann. Statist. 36 (2008), no. 4, 1693--1725. doi:10.1214/07-AOS519.

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