Publications and Preprints

We consider the estimation of a two dimensional continuous-discrete density function with applications to competing risks. We construct two new wavelet estimators (non-adaptive and adaptive) for the joint density function taking into account this special continuous-discrete structure. The rates of convergence of the proposed estimators are established under the $\mathbb{L}_2$ risk over Besov balls. Our main result proves that our adaptive wavelet estimator (based on hard thresholding) attains a sharp rate of convergence. A simulation study illustrates the usefulness of the proposed estimators.