Complexity-regularized multiresolution density estimation

Rebecca M. Willett, Robert D. Nowak

Abstract: The density estimation method proposed in this paper employs piecewise polynomial fits on adaptive dyadic partitions. The proposed estimator enjoys the minimax adaptivity associated with wavelet-based density estimators as well as the following additional advantages: estimates are guaranteed to be nonnegative, theoretical bounds provide an indication of performance even for small sample sizes, and the method can be extended to free-degree piecewise polynomial estimation, which allows the data to adaptively determine the smoothness of the underlying basis functions