Original Paper

Computational Statistics

, Volume 27, Issue 4, pp 757-777

First online:

Density estimation and comparison with a penalized mixture approach

  • Christian SchellhaseAffiliated withDepartment for Business Administration and Economics, Centre for Statistics, Bielefeld University
  • , Göran KauermannAffiliated withDepartment of Statistics, Ludwig-Maximilians-University Munich Email author 

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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 Komárek 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.


Density estimation Mixture density estimation Penalized spline smoothing ANOVA