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Application of Variational Analysis and Control Theory to Nonparametric Maximum Likelihood Estimation of a Density Function

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Variational Analysis and Generalized Differentiation in Optimization and Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 47))

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Abstract

In this chapter, we propose a new approach to the estimation of the probability density function based on the maximum likelihood method if it is known that the underlying density function is Lipschitz. We treat this problem as an optimal control problem and prove convergence results using techniques of variational analysis.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Penn State Harrisburg, Middletown, PA, 17057, USA

    Ilya Shvartsman

Authors
  1. Ilya Shvartsman
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Correspondence to Ilya Shvartsman .

Editor information

Editors and Affiliations

  1. School of Mathematics & Statistics, Division of Information Technology, University of South Australia, Mawson Lakes Blvd., Mawson Lakes, 5095, South Australia, Australia

    Regina S. Burachik

  2. , Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan R.O.C.

    Jen-Chih Yao

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Shvartsman, I. (2010). Application of Variational Analysis and Control Theory to Nonparametric Maximum Likelihood Estimation of a Density Function. In: Burachik, R., Yao, JC. (eds) Variational Analysis and Generalized Differentiation in Optimization and Control. Springer Optimization and Its Applications, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0437-9_10

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