Fold-up derivatives of set-valued functions and the change-set problem: a survey (Q1695752)
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scientific article; zbMATH DE number 6835997
| Language | Label | Description | Also known as |
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| English | Fold-up derivatives of set-valued functions and the change-set problem: a survey |
scientific article; zbMATH DE number 6835997 |
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Fold-up derivatives of set-valued functions and the change-set problem: a survey (English)
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8 February 2018
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\textit{E. V. Khmaladze} [J. Math. Anal. Appl. 334, No. 2, 1055--1072 (2007; Zbl 1127.49016)] introduced a set-valued derivative of a \(d\)-dimensional set-valued function (\(d \geq 1\)), called \textit{fold-up derivative}. This long review article discusses the geometric properties of such derivatives and applications to statistical testing of change-set problems (as in a change-point problem in one dimension). Two distributional convergence results involving Poisson point processes and one central limit theorem with limiting normal distribution are given. Extensions and variants of the fold-up derivative are also discussed.
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infinitesimal image analysis
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generalized functions
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fold-up derivatives
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local Steiner formula
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local point process
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set-valued mapping
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derivative set
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normal cylinder
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change-set problem
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central limit theorem
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