Book Chapter

Bivariate density estimation with restricted domains: working with oblique coordinates

In: Meira-Machado, L., Soutinho, G. (Eds.): Proceedings of the 34th International Workshop on Statistical Modelling, Guimarães, Portugal, July 7-12, 2019, volume II, 96–100
Statistical Modelling Society (2020)


Bivariate density estimation via P-splines is not straightforward if the domain of the density is restricted in a complex way. We propose an approach to estimate bivariate densities with restricted domains, based on the geometric structure of the density's support. We first change to an oblique coordinate system, where we can estimate the bivariate density using a spline basis on a rectangular grid. The estimated density is obtained by transforming back to the original plane. We show an application to simulated data which are modelled after patterns of first marital births.

The Max Planck Institute for Demographic Research (MPIDR) in Rostock is one of the leading demographic research centers in the world. It's part of the Max Planck Society, the internationally renowned German research society.