This paper presents a method for estimating the number of independent components in functional magnetic resonance imaging (fMRI) data. The method addresses the issue of sample dependence in fMRI data, which can lead to overestimation of the number of brain sources. The authors propose a subsampling scheme to obtain a set of effectively independent and identically distributed (i.i.d.) samples from the dependent data samples. They apply information-theoretic criteria (ITC) formulas to the effectively i.i.d. sample set for order selection. The method is tested on simulated data and fMRI data from a visuomotor task. The results show that the proposed method significantly improves the accuracy of order selection from dependent data and alleviates the overestimation of the number of brain sources due to the intrinsic smoothness and preprocessing of fMRI data. The authors also show that when ICA is performed at overestimated orders, the stability of the IC estimates decreases and the estimation of task-related brain activations shows degradation. The method is based on the entropy rate matching principle, which is used to identify effectively i.i.d. samples. The proposed method is applied to fMRI data from eleven subjects performing a visuomotor task. The results show that the order selection based on effectively i.i.d. samples is more accurate and stable than order selection based on the original data. The authors conclude that the proposed method improves the order selection performance of different ITCs and that performing ICA in an unnecessarily high dimensional subspace decreases the stability of ICA estimation and could degrade the integrity of the ICA representation on brain activations. The method is motivated by the characteristics of fMRI data, which are typically smoother than noise in the spatial domain. The authors also discuss the implications of the results for future research in order selection, including the study of the effects of finite sample size and the compensation of the effect of dependencies in the sample space.This paper presents a method for estimating the number of independent components in functional magnetic resonance imaging (fMRI) data. The method addresses the issue of sample dependence in fMRI data, which can lead to overestimation of the number of brain sources. The authors propose a subsampling scheme to obtain a set of effectively independent and identically distributed (i.i.d.) samples from the dependent data samples. They apply information-theoretic criteria (ITC) formulas to the effectively i.i.d. sample set for order selection. The method is tested on simulated data and fMRI data from a visuomotor task. The results show that the proposed method significantly improves the accuracy of order selection from dependent data and alleviates the overestimation of the number of brain sources due to the intrinsic smoothness and preprocessing of fMRI data. The authors also show that when ICA is performed at overestimated orders, the stability of the IC estimates decreases and the estimation of task-related brain activations shows degradation. The method is based on the entropy rate matching principle, which is used to identify effectively i.i.d. samples. The proposed method is applied to fMRI data from eleven subjects performing a visuomotor task. The results show that the order selection based on effectively i.i.d. samples is more accurate and stable than order selection based on the original data. The authors conclude that the proposed method improves the order selection performance of different ITCs and that performing ICA in an unnecessarily high dimensional subspace decreases the stability of ICA estimation and could degrade the integrity of the ICA representation on brain activations. The method is motivated by the characteristics of fMRI data, which are typically smoother than noise in the spatial domain. The authors also discuss the implications of the results for future research in order selection, including the study of the effects of finite sample size and the compensation of the effect of dependencies in the sample space.