Random closed sets

Molchanov, Ilya (2005). Random closed sets. In: Bilodeau, Michel; Meyer, Fernand; Schmitt, Michel (eds.) Space, structure and randomness. Lecture Notes in Statistics: Vol. 183 (pp. 135-149). Springer, New York 10.1007/0-387-29115-6_7

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Concepts and results involving random sets appeared in probabilistic and statistical literature long time ago. The origin of the modern concept of a random set goes as far back as the seminal book by A.N. Kolmogorov [22] (first published in 1933) where he laid out the foundations of probability theory. He wrote [22, p. 46] Let G be a measurable region of the plane whose shape depends on chance; in other words let us assign to every elementary event ξ of a field of probability a definite measurable plane region G. In modern terminology, G is said to be a random set, which is not necessarily closed, see [37, Sec. 2.5]. It should be noted also that even before 1933 statisticians worked with confidence regions that can be naturally described as random sets.

Item Type:

Book Section (Review Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Molchanov, Ilya

Subjects:

500 Science > 510 Mathematics

ISBN:

978-0-387-20331-7

Series:

Lecture Notes in Statistics

Publisher:

Springer, New York

Language:

English

Submitter:

Ilya Molchanov

Date Deposited:

09 Aug 2016 07:59

Last Modified:

09 Aug 2016 07:59

Publisher DOI:

10.1007/0-387-29115-6_7

URI:

https://boris.unibe.ch/id/eprint/85372

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