Abstract
Mathematical statistics is a nice source of nonstandard variational problems. As an example we can mention the famous Neyman—Pearson lemma on hypothesis testing: in optimization language it is a variational problem with integral type functional (not including derivatives) subject to specific constraints. In this paper we deal with variational problems of another kind arising in such areas of statistics as parameter estimation and nonparametric regression. Among them there are such nonstandard problems as minimization of a functional which is a ratio of two integrals, minimization of a matrix-valued criteria, finding a saddle point of a functional over some classes of functions etc. Some of these problems can be solved in explicit form by use of a technique which is untypical for the classical calculus of variations.
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© 1990 Springer Science+Business Media New York
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Polyak, B.T. (1990). Variational Problems Arising in Statistics. In: Perspectives in Control Theory. Progress in Systems and Control Theory, vol 2. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-2105-8_17
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DOI: https://doi.org/10.1007/978-1-4757-2105-8_17
Publisher Name: Birkhäuser, Boston, MA
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