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• W2314657509 abstract "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 emors of the estimate, and some large sample approximations am derived. Procedures for choosing a smoothing parameter are developed and illustrated by simulations. The estimation of peak area in the presence of a baseline of unknown shape is a common problem in nuclear and other spectroscopies. In this paper we analyze some of the properties of a generalization of a procedure proposed by Currie [2]' and note that the procedure has a certain minimax optimality. We first introduce the problem and some notation. We suppose that counts are accumulated in n channels over a length of time T, and that the total number of counts has mean p, = vT, where v = mean counting rate per unit time. We let y, denote the proportional count in the j'b channel, i.e. the total count in the channel divided by >, and we assume that v; = P.,.j + + Ej j =1.. Here, r = ('Y1 .. , yn)f is a vector representing a peak shape, which is assumed known (F might be known from theory or from measurement of pure specimens, for example), P. is its unknown amplitude, which we wish to determine, and Pi, is the unknown baseline mean in the j' channel. The 6;s are random counting errors with mean zero and nonsingular covariance matrix L- W-' where W is a matrix which is assumed to be known. (In applications, W is typically estimated rather than known. An application of the 8-method [7] to the perturbation thus introduced shows that the asymptotic means and variances are unchanged.) In vector notation the model can be written Y= [r:i]p + e" @default.
• W2314657509 created "2016-06-24" @default.
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• W2314657509 date "1982-01-01" @default.
• W2314657509 modified "2023-10-05" @default.
• W2314657509 title "An Approach to Peak Area Estimation" @default.
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• W2314657509 doi "https://doi.org/10.6028/jres.087.007" @default.
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