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A statistical estimate of the structure of multi-extremal problems

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Abstract

The solution of ak-extremal problem is defined as the set of pairs (x *i , θi),i = 1, ⋯ ,k, where x *t isi th local minimum andθ i is the volume of the set of attraction of this minimum. A Bayesian estimate ofk and (θ 1 , ⋯ , θ k ) is constructed.

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References

  1. W. Feller,An introduction to probability theory and its applications, Vol. I, second edition (Wiley, New York, 1961).

    Google Scholar 

  2. N.L. Johnson and S. Kotz,Distributions in statistics: continuous multivariate distributions (Wiley, New York, 1972).

    Google Scholar 

  3. G. Schwarz, “Estimating the dimension of a model”,Annals of Statistics 6 (1978) 461–464.

    Google Scholar 

  4. M. Sobel, V.R.R. Uppuluri and K. Frankowski,Selected tables in mathematical statistics, Vol. IV (Am. Math. Soc., Providence, R.I., 1977).

    Google Scholar 

  5. S. Zacks,The theory of statistical inference (Wiley, New York, 1971).

    Google Scholar 

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This paper has been written while the author was a CNR visiting professor at the Institute of Mathematics of the Milano University.

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Zieliński, R. A statistical estimate of the structure of multi-extremal problems. Mathematical Programming 21, 348–356 (1981). https://doi.org/10.1007/BF01584254

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  • DOI: https://doi.org/10.1007/BF01584254

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