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Groeneboom, P. and Wellner, J.A. (1992) Information Bounds and Nonparametric Maximum Likelihood Estimation. Vol. 19, Springer Science and Business Media, Berlin/Heidelberg.

has been cited by the following article:

• TITLE: L0 Regularization for the Estimation of Piecewise Constant Hazard Rates in Survival Analysis

  AUTHORS: Olivier Bouaziz, Grégory Nuel

  KEYWORDS: Adaptive Ridge Procedure, Hazard Rate Estimation, Penalized Likelihood, Piecewise Constant Hazard, Survival Analysis

  JOURNAL NAME: Applied Mathematics, Vol.8 No.3, March 30, 2017

  ABSTRACT: In a survival analysis context, we suggest a new method to estimate the piecewise constant hazard rate model. The method provides an automatic procedure to find the number and location of cut points and to estimate the hazard on each cut interval. Estimation is performed through a penalized likelihood using an adaptive ridge procedure. A bootstrap procedure is proposed in order to derive valid statistical inference taking both into account the variability of the estimate and the variability in the choice of the cut points. The new method is applied both to simulated data and to the Mayo Clinic trial on primary biliary cirrhosis. The algorithm implementation is seen to work well and to be of practical relevance.