Constructing prediction intervals for the age distribution of deaths

We introduce a model-agnostic procedure to construct prediction intervals for the age distribution of deaths. The age distribution of deaths is an example of constrained data, which are nonnegative and have a constrained integral. A centered log-ratio transformation and a cumulative distribution function transformation are used to remove the two constraints, where the latter transformation can also handle the presence of zero counts. Our general procedure divides data samples into training, validation, and testing sets. Within the validation set, we can select an optimal tuning parameter by calibrating the empirical coverage probabilities to be close to their nominal ones. With the selected optimal tuning parameter, we then construct the pointwise prediction intervals using the same models for the holdout data in the testing set. Using Japanese age- and sex-specific life-table death counts, we assess and evaluate the interval forecast accuracy with a suite of functional time-series models.