Auditory evoked potential (AEP) recordings have been analyzed through independent component analysis (ICA) in the literature; however, the performance varies depending on the ICA algorithms used. There are very few studies that concentrate on the optimum parameter selection for estimating the AEP components reliably, while also recovering the specific artifact generated with the normal functioning of a cochlear implant (CI). The objective of this research is to determine which ICA algorithm, high-order statistics (HOS)-based or second-order statistic (SOS)-based, is more plausible to remove this artifact and estimate the AEP. The optimal parameters of three such ICA algorithms for estimating the components from a database of recordings were determined, and then the estimates for the AEP and CI artifact were compared using each method. All the algorithms estimate the CI artifact reasonably well, although only one SOS algorithm is better positioned to estimate the AEP; this is primarily because it uses the temporal structure of this signal as part of the ICA process.