期刊
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
卷 77, 期 7, 页码 561-574出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10629360600569097
关键词
non-parametric density estimation; shape restriction; interior point method; iterative convex minorant algorithm; Newton method on subspace
We consider the problem of estimating a density function that is assumed to be log- concave. This semi-parametric model includes many well- known parametric classes; such as Normal, Gamma, Laplace, Logistic, Beta or Extreme value distributions, for specific parameter ranges. It is known that the maximum likelihood estimator for the log- density is always a piecewise linear function with at most as many knots as observations, but typically much less. We show that this property can be exploited to design a linearly constrained optimization problem whose iteratively calculated solution yields the estimator. We compare several standard and one recently proposed algorithm regarding their performance on this problem.
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