Abstract
In this work we will explore the theoretical and practical aspects of nonparametric
exponential deconvolution in the two-dimensional setting. After a transformation, exponential
deconvolution can be used to estimate a decreasing density from direct observations.
First, we will rigorously derive an inversion formula that can be implemented in an actual
software implementation. We will then proceed with summarizing some of the known
statistical properties of nonparametric kernel density estimators. Finally, we will combine the
obtained results and construct, implement and test an exponential deconvolution method
based on kernel estimators. An interesting application for estimation of decreasing densities
will be pointed out and elaborated.
Keywords: deconvolution, decreasing densities, kernel estimation.