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- Title
Response and predictor folding to counter symmetric dependency in dimension reduction.
- Authors
Prendergast, L.A.; Garnham, A.L.
- Abstract
In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualisation in a low-dimensional framework. However, some popular dimension reduction methodologies fail to achieve this aim when faced with a problem often referred to as symmetric dependency. In this paper we show how vastly superior results can be achieved when carrying out response and predictor transformations for methods such as least squares and sliced inverse regression. These transformations are simple to implement and utilise estimates from other dimension reduction methods that are not faced with the symmetric dependency problem. We highlight the effectiveness of our approach via simulation and an example. Furthermore, we show that ordinary least squares can effectively detect multiple dimension reduction directions. Methods robust to extreme response values are also considered.
- Subjects
SYMMETRIC matrices; SYMMETRIC-key algorithms; LEAST squares; ISOTONIC regression; DIMENSIONAL reduction algorithms
- Publication
Australian & New Zealand Journal of Statistics, 2016, Vol 58, Issue 4, p515
- ISSN
1369-1473
- Publication type
Article
- DOI
10.1111/anzs.12170