Optimal spline smoothing of fMRI time series by generalized cross-validation

Linear parametric regression models of fMRI time series have correlated residuals. One approach to address this problem is to condition the autocorrelation structure by temporal smoothing. Smoothing splines with the degree of smoothing selected by generalized cross-validation (GCV-spline) provide a method to find an optimal smoother for an fMRI time series. The purpose of this study was to determine if GCV-spline of fMRI time series yields unbiased variance estimates of linear regression model parameters. GCV-spline was evaluated with a real fMRI data set and bias of the variance estimator was computed for simulated time series with autocorrelation structures derived from fMRI data. This study only considered fMRI experimental designs of boxcar type. The results from the real data suggest that GCV-spline determines appropriate amounts of smoothing. The simulations show that the variance estimates are, on average, unbiased. The unbiased variance estimates come at some cost to signal detection efficiency. This study demonstrates that GCV-spline is an appropriate method for smoothing fMRI time series.