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Title: A fast algorithm for univariate log-concave density estimation Authors:  Yong Wang - University of Auckland (New Zealand) [presenting]
Abstract: A new fast algorithm is proposed and studied for computing the nonparametric maximum likelihood estimate of a univariate log-concave density. In each iteration, the newly extended algorithm includes, if necessary, new knots in aid of a gradient function, renews the changes of slope at all knots via a quadratically convergent method and removes the knots at which the changes of slope become zero. Theoretically, the characterisation of the nonparametric maximum likelihood estimate is studied and the algorithm is guaranteed to converge to the unique maximum likelihood estimate. Numerical studies show that it outperforms other algorithms that are available in the literature. Applications to some real-world financial data are also given.