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We consider the problem, arising in nuclear spectroscopy, of estimating peak areas in the presence of a baseline of unknown shape. We analyze a procedure that chooses the baseline to be as smooth as is consistent with the data and note that the estimates have a certain minimax optimality. Expressions are developed for the systematic and random errors of the estimate, and some large sample approximations are derived. Procedures for choosing a smoothing parameter are developed and illustrated by simulations.
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