Objective: The Temporal Response Function (TRF) is a linear model of neural activity time-locked to continuous stimuli, including continuous speech. TRFs based on speech envelopes typically have distinct components that have provided remarkable insights into the cortical processing of speech. However, current methods may lead to less than reliable estimates of single-subject TRF components. Here, we compare two established methods, in TRF component estimation, and also propose novel estimation algorithms that utilize prior knowledge of these components, bypassing the full TRF estimation. Methods: We compared two established algorithms, ridge and boosting, and two novel algorithms based on Subspace Pursuit and Expectation Maximization, which directly estimate TRF components given plausible assumptions regarding component characteristics. Single-channel, multi-channel, and source-localized TRFs were fit on simulations and real magnetoencephalographic data. Performance metrics included model fit and component estimation accuracy. Results: Boosting and ridge have comparable performance in component estimation. The novel algorithms outperformed the others in simulations, but not on real data, possibly due to the plausible assumptions not actually being met. Ridge had marginally better model fits on real data, but also more spurious TRF activity. Conclusion: Results indicate that both smooth (ridge) and sparse (boosting) algorithms perform comparably at TRF component estimation. The SP and EM algorithms may be accurate, but rely on assumptions of component characteristics. Significance: This systematic comparison establishes the suitability of widely used and novel algorithms for estimating robust TRF components, which is essential for improved subject-specific investigations into the cortical processing of speech.