Assume we have a dataset, Z say, from the joint distribution of random variables X and Y , and two further, independent datasets, X and Y, from the marginal distributions of X and Y , respectively. We wish to combine X, Y and Z, so as to construct an estimator of the joint density. This problem...

Assume we have a dataset, Z say, from the joint distribution of random variables X and Y , and two further, independent datasets, X and Y, from the marginal distributions of X and Y , respectively. We wish to combine X, Y and Z, so as to construct an estimator of the joint density. This problem...

The objective of this paper is to estimate a bivariate density nonparametrically from a dataset from the joint distribution and datasets from one or both marginal distributions. We develop a copula-based solution, which has potential benefits even when the marginal datasets are empty. For...