  The B-spline copula function is defined by a linear combination of elements
of the normalized B-spline basis. We develop a modified EM algorithm, to
maximize the penalized log-likelihood function, wherein we use the smoothly
clipped absolute deviation (SCAD) penalty function for the penalization term.
We conduct simulation studies to demonstrate the stability of the proposed
numerical procedure, show that penalization yields estimates with smaller
mean-square errors when the true parameter matrix is sparse, and provide
methods for determining tuning parameters and for model selection. We analyze
as an example a data set consisting of birth and death rates from 237
countries, available at the website, ''Our World in Data,'' and we estimate the
marginal density and distribution functions of those rates together with all
parameters of our B-spline copula model.
