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Computing Maximum Likelihood Estimators of Convex Density Functions

Collection
  • Cahiers de recherche; 1995.16
Publication date1995
Abstract

e consider the problem of estimating a density function that is known in advance to be convex. The maximum likelihood estimator is then the solution of linearly constrained convex minimization problem. This problem turns out to be numerically difficult. We show that interior point algorithms perform well on this class of optimization problems, though for large samples, numerical difficulties are still encountered. To eliminate those difficulties, we propose a clustering scheme that is reasonable from a statistical point of view. We display results for problems with up to 40000 observations. We also give a typical picture of the estimated density: a piece wise linear function, with very few pieces only

Citation (ISO format)
TERLAKY, T., VIAL, Jean-Philippe. Computing Maximum Likelihood Estimators of Convex Density Functions. 1995
Identifiers
  • PID : unige:5978
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