Bivariate Uniform Deconvolution

We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations. By substituting a kernel density estimator of the density of the observations we then get four different estimators. Next we construct an asymptotically optimal convex combination of these four estimators. Expansions for the bias, variance, as well as asymptotic normality, are derived. Some simulated examples are presented.