The paper addresses the challenge of order selection in independent component analysis (ICA) for functional magnetic resonance imaging (fMRI) data, which is crucial for reducing over/underfitting. Due to the high dimensionality and noise level of fMRI data, traditional information-theoretic criteria (ITCs) based on independent and identically distributed (i.i.d.) samples are not suitable for dependent data. The authors propose a subsampling scheme to obtain effectively i.i.d. samples from dependent fMRI data and apply ITC formulas to these samples for order selection. They demonstrate that this method significantly improves the accuracy of order selection on simulated data and fMRI data from a visuomotor task, alleviating overestimation of the number of brain sources due to intrinsic smoothness and preprocessing. The proposed method is validated using the ICASSO software package, showing that overestimation of the order leads to decreased stability and degradation in task-related brain activation estimation.The paper addresses the challenge of order selection in independent component analysis (ICA) for functional magnetic resonance imaging (fMRI) data, which is crucial for reducing over/underfitting. Due to the high dimensionality and noise level of fMRI data, traditional information-theoretic criteria (ITCs) based on independent and identically distributed (i.i.d.) samples are not suitable for dependent data. The authors propose a subsampling scheme to obtain effectively i.i.d. samples from dependent fMRI data and apply ITC formulas to these samples for order selection. They demonstrate that this method significantly improves the accuracy of order selection on simulated data and fMRI data from a visuomotor task, alleviating overestimation of the number of brain sources due to intrinsic smoothness and preprocessing. The proposed method is validated using the ICASSO software package, showing that overestimation of the order leads to decreased stability and degradation in task-related brain activation estimation.