The generalized cross entropy method, with applications to probability density estimation
Botev, Zdravko I. and Kroese, Dirk P. (2011) The generalized cross entropy method, with applications to probability density estimation. Methodology and Computing in Applied Probability, 131: 1-27. doi:10.1007/s11009-009-9133-7
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Nonparametric density estimation aims to determine the sparsest model that explains a given set of empirical data and which uses as few assumptions as possible. Many of the currently existing methods do not provide a sparse solution to the problem and rely on asymptotic approximations. In this paper we describe a framework for density estimation which uses information-theoretic measures of model complexity with the aim of constructing a sparse density estimator that does not rely on large sample approximations. The effectiveness of the approach is demonstrated through an application to some well-known density estimation test cases.