Integral trimmed regions
We define a new family of central regions with respect to a probability measure. They are induced by a set or a family of sets of functions and we name them integral trimmed regions. The halfspace trimming and the zonoid trimming are particular cases of integral trimmed regions. We focus our work on the derivation of properties of such integral trimmed regions from conditions satisfied by the generating classes of functions. Further we show that, under mild conditions, the population integral trimmed region of a given depth can be characterized in terms of certain regions based on empirical distributions.
Volume (Year): 96 (2005)
Issue (Month): 2 (October)
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- Masse, J. C. & Theodorescu, R., 1994. "Halfplane Trimming for Bivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 188-202, February.
- Fernández, Ignacio Cascos & Molchanov, Ilya, 2003. "A stochastic order for random vectors and random sets based on the Aumann expectation," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 295-305, July.