Smoothing densities under shape constraints

Abstract

In Davies and Kovac (2004) the taut string method was proposed for calculating a density which is consistent with the data and has the minimum number of peaks. The main disadvantage of the taut string density is that it is piecewise constant. In this paper a procedure is presented which gives a smoother density by minimizing the total variation of a derivative of the density subject to the number, positions and heights of the local extreme values obtained from the taut string density. 2000 MSC primary: 62G07