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A profile likelihood algorithm is proposed for quantitative shotgun proteomics to infer the abundance ratios of proteins from the abundance ratios of isotopically labeled peptides derived from proteolysis. Previously, we have shown that the estimation variability and bias of peptide abundance ratios can be predicted from their profile signal-to-noise ratios. Given multiple quantified peptides for a protein, the profile likelihood algorithm probabilistically weighs the peptide abundance ratios by their inferred estimation variability, accounts for their expected estimation bias, and suppresses contribution from outliers. This algorithm yields maximum likelihood point estimation and profile likelihood confidence interval estimation of protein abundance ratios. This point estimator is more accurate than an estimator based on the average of peptide abundance ratios. The confidence interval estimation provides an "error bar" for each protein abundance ratio that reflects its estimation precision and statistical uncertainty. The accuracy of the point estimation and the precision and confidence level of the interval estimation were benchmarked with standard mixtures of isotopically labeled proteomes. The profile likelihood algorithm was integrated into a quantitative proteomics program, called ProRata, freely available at www.MSProRata.org.