Density estimation and comparison with a penalized mixture approach

Schellhase C, Kauermann G. Density estimation and comparison with a penalized mixture approach. Computational Statistics. 2012;27(4):757-777.The paper presents smooth estimation of densities utilizing penalized splines. The idea is to represent the unknown density by a convex mixture of basis densities, where the weights are estimated in a penalized form. The proposed method extends the work of Komarek and Lesaffre (Comput Stat Data Anal 52(7):3441-3458, 2008) and allows for general density estimation. Simulations show a convincing performance in comparison to existing density estimation routines. The idea is extended to allow the density to depend on some (factorial) covariate. Assuming a binary group indicator, for instance, we can test on equality of the densities in the groups. This provides a smooth alternative to the classical Kolmogorov-Smirnov test or an Analysis of Variance and it shows stable and powerful behaviour