Efficient estimation of smooth distributions from coarsely grouped data.
Bottom Line: Optimal values of the smoothing parameter are chosen by minimizing Akaike's Information Criterion.We demonstrate the performance of this method in a simulation study and provide several examples that illustrate the approach.Wide, open-ended intervals can be handled properly.
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Mentions: We first apply the approach to deaths from diseases of the circulatory system. The results are shown in Figure 2. The open-ended age class collects the observations made for individuals older than the starting age for the interval (here, age 85 years). Although in theory the tail area could be unlimited, in most applications there is a maximal number beyond which no observation is expected or is even possible. As the penalized composite link model smoothly redistributes the grouped observations into the tail area, such information, if available, should be provided. For the present application, the age of 115 years was set as the maximum, and the histogram was complemented with an age group from 115 to 130 years with 0 counts. The penalized composite link model can easily deal with longer stretches of 0 counts.Figure 2.