Constructing prediction intervals for the age distribution of deaths

TL;DR

This paper presents a model-agnostic method for constructing prediction intervals for age-at-death distributions, effectively handling data constraints and zero counts, validated with Japanese mortality data.

Contribution

Introduces a novel, model-agnostic procedure using transformations and calibration for accurate prediction intervals of constrained death age distributions.

Findings

Effective handling of zero counts in data

Calibration improves coverage probability accuracy

Method validated with Japanese mortality data

Abstract

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.