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Raman spectroscopy is a powerful and effective technique for analyzing and identifying the chemical composition of a substance. Two types of Raman spectra estimation algorithms exist: supervised and unsupervised. In this paper, we perform a comparative analysis of five supervised algorithms for estimating Raman spectra. We describe a realistic measurement model for a dispersive Raman measurement device and observe that the measurement error variances vary significantly with bin index. Monte Carlo analyses with simulated measurements are used to calculate the bias root mean square error, and computational time for each algorithm. Our analyses show that it is important to use correct measurement weights and enforce the nonnegative constraint in parameter estimation.