Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The expected convex hull trimmed regions of a sample
Computational Statistics
Computing zonoid trimmed regions of dimension d2
Computational Statistics & Data Analysis
Trimmed regions induced by parameters of a probability
Journal of Multivariate Analysis
| Hi-index | 0.00 |
A general notion of trimmed regions for empirical distributions in d-space is introduced. The regions are called weighted-mean trimmed regions. They are continuous in the data as well as in the trimming parameter. Further, these trimmed regions have many other attractive properties. In particular they are subadditive and monotone which makes it possible to construct multivariate measures of risk based on these regions. Special cases include the zonoid trimming and the ECH (expected convex hull) trimming. These regions can be exactly calculated for any dimension. Finally, the notion of weighted-mean trimmed regions extends to probability distributions in d-space, and a law of large numbers applies.