## Institute of Mathematical Statistics Lecture Notes - Monograph Series

- Optimality
- 2009, 190-215

### Nonparametric Estimation of Hemodynamic Response Function: A Frequency Domain Approach

Ping Bai, Young Truong, and Xuemei Huang

#### Abstract

Hemodynamic response function (HRF) has played an important role in many recent functional magnetic resonance imaging (fMRI) based brain studies where the main focus is to investigate the relationship between stimuli and the neural activity. Standard statistical analysis of fMRI data usually calls for a “canonical” model of HRF, but it is uncertain how well this fits the actual HRF. The objective of this paper is to exploit the experimental designs by modeling the stimulus sequences using stochastic point processes. The identification of the stimulus-response relationship will be conducted in the frequency domain, which will be facilitated by fast Fourier transforms (FFT). The usefulness of this approach will be illustrated using both simulated and real human brain data. Under regularity conditions, it is shown that the estimated HRF possesses an asymptotic normal distribution.

#### Chapter information

**Source***Optimality: The Third Erich L. Lehmann Symposium* (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009)

**Dates**

First available in Project Euclid: 3 August 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.lnms/1249305330

**Digital Object Identifier**

doi:10.1214/09-LNMS5712

**Mathematical Reviews number (MathSciNet)**

MR2681664

**Zentralblatt MATH identifier**

1271.62061

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

**Keywords**

fMRI hemodynamic response function transfer function model point process spectral analysis

**Rights**

Copyright © 2009, Institute of Mathematical Statistics

#### Citation

Rojo, Javier. Nonparametric Estimation of Hemodynamic Response Function: A Frequency Domain Approach. Optimality, 190--215, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-LNMS5712. https://projecteuclid.org/euclid.lnms/1249305330

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