Orthogonal projection in teaching regression and financial mathematics
| aut.relation.issue | 1 | |
| aut.relation.volume | 18 | |
| dc.contributor.author | Kachapova, F | |
| dc.contributor.author | Kachapov, I | |
| dc.date.accessioned | 2013-06-07T07:28:10Z | |
| dc.date.available | 2013-06-07T07:28:10Z | |
| dc.date.copyright | 2010 | |
| dc.date.issued | 2010 | |
| dc.description.abstract | Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear regression in finance is described as an example of practical applications of the population regression model. The paper also describes a geometric approach to teaching the topic of finding an optimal portfolio in financial mathematics. The approach is to express the optimal portfolio through an orthogonal projection in Euclidean space. This allows replacing the traditional solution of the problem with a geometric solution, so the proof of the result is merely a reference to the basic properties of orthogonal projection. This method improves the teaching of the topic by avoiding tedious technical details of the traditional solution such as Lagrange multipliers and partial derivatives. The described method is illustrated by two numerical examples. | |
| dc.identifier.citation | Journal of Statistics Education, vol.18(1) | |
| dc.identifier.issn | 1069-1898 | |
| dc.identifier.roid | 13857 | en_NZ |
| dc.identifier.uri | https://hdl.handle.net/10292/5430 | |
| dc.publisher | ASA Publications | |
| dc.relation.uri | http://www.amstat.org/publications/jse/v18n1/kachapova.pdf | |
| dc.rights | Copyright © 2010 by Farida Kachapova and Ilias Kachapov all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor. | |
| dc.rights.accessrights | OpenAccess | |
| dc.subject | Population model of regression | |
| dc.subject | Regression in finance | |
| dc.subject | Optimal portfolio | |
| dc.subject | Minimizing risk | |
| dc.title | Orthogonal projection in teaching regression and financial mathematics | |
| dc.type | Journal Article | |
| pubs.elements-id | 13495 | |
| pubs.organisational-data | /AUT | |
| pubs.organisational-data | /AUT/Design & Creative Technologies | |
| pubs.organisational-data | /AUT/Design & Creative Technologies/School of Computing & Mathematical Science |