Efficient estimation of smooth distributions from coarsely grouped data.
Bottom Line: This maximization is performed efficiently by a version of the iteratively reweighted least-squares algorithm.Optimal values of the smoothing parameter are chosen by minimizing Akaike's Information Criterion.Wide, open-ended intervals can be handled properly.
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Mentions: The same approach was applied to the age-at-death distribution for the other 3 causes of death. The results are illustrated in Figure 3. These 3 distributions were chosen because they allow us to demonstrate the performance of the method in various circumstances. The age-at-death distribution for neoplasms (Figure 3A) is unimodal, whereas the age-at-death distribution for infectious and parasitic diseases (Figure 3C) has a bimodal shape. Because we assume only that the latent distribution γ is smooth, the model performs well in either case, independent of the shape of the distribution. Furthermore, the sample sizes of these age-at-death distributions vary considerably: There were 9,643 deaths due to diseases of the blood and immune system (Figure 3B) but 582,219 deaths due to neoplasms—60 times as many. These differences in sample size do not undermine the accuracy of the obtained estimates. Because of the large sample sizes in these examples, standard errors were very narrow, and confidence intervals could hardly be seen, so we did not include them in the figures.Figure 3.