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MINIMAL ENCLOSING PARALLELEPIPED IN PARAMETRIC ESTIMATION OF MULTIDIMENSIONAL UNIFORM DISTRIBUTION
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MINIMAL ENCLOSING PARALLELEPIPED IN PARAMETRIC ESTIMATION OF MULTIDIMENSIONAL UNIFORM DISTRIBUTION
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Nikolai Kiselev 
Edition
Volume 49 Issue 1
Pages
119-128
Abstract

The linear model of generating a multidimensional random value with uniform distribution in a parallelepiped is discussed. Maximum likelihood principle in problem of parametric estimation is formulated as a principle of the minimal volume. In general case, the distinctive property of a minimal volume parallelepiped, enclosing all set of observations, is proved. On the basis of this property the algorithm of combinatorial class to find this parallelepiped is proposed. The results of numerical experiment on problem of estimation center and covariance matrix are represented for two-dimensional uniform distributed random value. In this experiment, the efficiency of minimum volume estimator is shown to be higher than that of a classical method of the moments.

Keywords
enclosing minimal volume parallelepiped, multidimensional uniform distribution, maximum likelihood estimator
Date of publication
01.01.2013
Number of purchasers
1
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823
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Additional sources and materials

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Vajnshtejn A.D. (1990). Postroenie minimal'nogo ob'emlyuschego parallelogramma // Diskretnaya matematika. T. 2. Vyp. 4.


Gol'shtejn E.G. (1999). Dvojstvennyj dekompozitsionnyj metod resheniya obschej zadachi drobno-linejnogo programmirovaniya // Ehkonomika i mat. metody. T. 35. Vyp. 1.


Dehjvid G. (1979). Poryadkovye statistiki. M.: Nauka.


Kiselev N.I. (2010). Al'ternativnye metody otsenki glavnykh komponent // Prikladnaya ehkonometrika. T. 8. Vyp. 3.


Kramer G. (1947). Matematicheskie metody statistiki. M.: Mir.


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Vivien F., Wicker N. (2004). Minimal Enclosing Parallelepiped in 3D. Computational Geometry // Theory and applications. Vol. 29.

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