English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

The $k$ principal points of a random vector $\mathbf{X}$ are defined as a setof points which minimize the expected squared distance between $\mathbf{X}$ andthe nearest point in the set. They are thoroughly studied in Flury (1990,1993), Tarpey (1995) and Tarpey, Li and Flury (1995). For their treatment, theexamination is usually restricted to the family of elliptical distributions. Inthis paper, we present an extension of the previous results to the functionalelliptical distribution case, i.e., when dealing with random elements over aseparable Hilbert space ${\cal H}$. Principal points for gaussian processeswere defined in Tarpey and Kinateder (2003). In this paper, we generalize theconcepts of principal points, self-consistent points and ellipticaldistributions so as to fit them in this functional framework. Results linkingself-consistency and the eigenvectors of the covariance operator arere-obtained in this new setting as well as an explicit formula for the $k=2$case so as to include elliptically distributed random elements in ${\cal H}$.

Principal points and elliptical distributions from the multivariate setting to the functional case