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: To demonstrate the performance of the extended approach, we apply it to diseases of the circulatory system and compare estimated and original age-specific death rates. The exposure data were taken from the Human Mortality Database (21). They were provided by single year of age from 0 to 109 years, with a last age class of ≥110 years. We produced ungrouped estimates of the exposures after grouping them in the same age classes as the event counts. Again, the results are reassuring (Figure 4A). In Figure 4B and 4C, 2 versions of estimated death rates are shown. In Figure 4B, only the event counts were ungrouped, but the exposures were taken by single year of age from the Human Mortality Database. In Figure 4C, both the number of events and the exposures were ungrouped. First, the ungrouped exposures were inserted into the composition matrix C, and the rates were estimated from this second penalized composite link model. The model succeeds in producing accurate results not only when the events are binned in intervals but also when the exposure numbers come in age groups. In both cases, the steep decline in death rates after age 0 years counteracts the idea of smoothness that underlies the penalized composite link model; however, this feature could be captured by a single point component.Figure 4.