Volume 44 - Article 45 | Pages 1085–1114 Editor's Choice Author has provided data and code for replicating results

D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties

By Carl Schmertmann

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Date received:02 Aug 2020
Date published:01 Jun 2021
Word count:6634
Keywords:mortality estimates, penalized likelihood, splines
Additional files:readme.44-45 (text file, 1 kB)
 demographic-research.44-45 (zip file, 290 MB)


Background: High-dimensional parametric models with penalized likelihood functions strike a good balance between bias and variance for estimating continuous age schedules from large samples. The penalized spline (P-spline) approach is particularly useful for these purposes, but it in small samples it can often produce implausible age schedule estimates.

Objective: I propose and evaluate a new type of P-spline model for estimating demographic rate schedules. These estimators, which I call D-splines, regularize and smooth high-dimensional splines by using demographic patterns rather than generic mathematical rules.

Methods: I compare P-spline estimates of age-specific mortality rates to three alternative D-spline estimators, over a large number of simulated small populations with known rates. The penalties for the D-spline estimators are derived from patterns in the Human Mortality Database.

Results: For mortality estimates in small populations, D-spline estimators generally have lower errors than standard P-splines.

Conclusions: Using penalties based on demographic information about patterns and variability in rate schedules improves P-spline estimators for small populations.

Contribution: This paper expands demographers' toolkit by developing a new category of P-spline estimators that are more reliable for estimating mortality in small populations.

Author's Affiliation

Carl Schmertmann - Florida State University, United States of America [Email]

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