Compositional Loess modeling
Author
Editor
- J.J. Egozcue
- R. Tolosana-Delgado
- M.I. Ortego
Summary, in English
We define a weighted least squares estimation for compositional data, C-WLS. In WLS the sum of the weighted squared Euclidean distances between the observed and the estimated values is minimized. In C-WLS we minimize the weighted sum of the squared simplicial distances (Aitchison, 1986, p. 193) between the observed compositions and their estimates.
We then define a compositional locally weighted regression, C-Loess. Here a composition is assumed to be explained by a real valued (multivariate) variable. For an arbitrary number of data points x<sub>i</sub> we for each x<sub>i</sub> fit a dth degree polynomial in x<sub>i</sub> yielding an estimate ŷ<sub>i</sub> of the composition y<sub>i</sub>. We use C-WLS to fit the polynomial giving the largest weights to the points x<sub>k</sub> (k = 1, ..., n) closest to x<sub>i</sub>.
Finally the C-Loess is applied to Swedish opinion poll data to create a poll-of-polls time series. The results are compared to previous results not acknowledging the compositional structure of the data.
Department/s
Publishing year
2011
Language
English
Publication/Series
Proceedings of the 4th International Workshop on Compositional Data Analysis
Full text
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Links
Document type
Conference paper
Topic
- Probability Theory and Statistics
Conference name
CoDaWork'11
Conference date
2011-05-10 - 2011-05-13
Conference place
Sant Feliu de Guixols, Girona, Spain
Status
Published
ISBN/ISSN/Other
- ISBN: 978-84-87867-76-7