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Paper: Bias-Free Parameter Estimation with Few Counts, by Iterative Chi-Squared %chi (2) Minimization
Volume: 77, Astronomical Data Analysis Software and Systems IV
Page: 331
Authors: Kearns, K.; Primini, F.; Alexander, D.
Abstract: We present a modified chi (2) fitting technique, %which is useful for fitting models to binned data with few counts per bin. We demonstrate through numerical simulations that model parameters estimated with our technique are essentially bias-free, even when the average number of counts per bin is ~ 1. This is in contrast to the results from traditional chi (2) techniques, which exhibit significant biases in such cases (see, for example, Nousek & Shue 1989; Cash 1979). Moreover, our technique can explicitly handle bins with 0 counts, obviating the need to ignore such bins or rebin the data. We conclude with a discussion of the problem of estimating goodness-of-fit in the limit of few counts using our modified chi (2) statistic.
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