Ordering multivariate observations by data depth

Title

Ordering multivariate observations by data depth

 Author

Dijkshoorn, Michel (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Statistics)

Contributor

Cai, J. (mentor) ORCID 0000-0003-3286-2126

 Degree granting institution

Delft University of Technology

 Programme

Applied Mathematics

 Date

2019-07-08

 Abstract

In this thesis the theory of depth functions is researched. Depth functions are functions that measure data depth and order multivariate observations. Two depth functions are discussed: the halfspace and simplicial depth function. The halfspace depth of a point is defined as the smallest probability for which a closed halfspace contains that point. The simplicial depth of a point is defined as the probability of that point being contained in a simplex for which its vertices are independent and identically distributed. Contours allow us to visualize these depth functions. This theory is applied to simulations with multivariate distributions and to weather statistics.

 Subject

Statistics
Extreme Value Theory
Data analysis

 To reference this document use:

http://resolver.tudelft.nl/uuid:decfc4b0-dc20-44f4-a2a6-9e6e2abc6e85

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2019 Michel Dijkshoorn
Files
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