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Compositional Loess Modelling

Cleveland (1979) is usually credited with the introduction of the locally weighted regression, Loess. The concept was further developed by Cleveland and Devlin (1988). The general idea is that for an arbitrary number of explanatory data points xi the value of a dependent variable is estimated ˆyi . The ˆyi is the fitted value from a dth degree polynomial in xi . (In practice often d = 1.) The ˆyi is fitted using weighted least squares, WLS, where the points xk (k = 1, . . . , n) closest to xi are given the largest weights. 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 xi we for each xi fit a dth degree polynomial in xi yielding an estimate ˆyi of the composition yi . We use C-WLS to fit the polynomial giving the largest weights to the points xk (k = 1, . . . , n) closest to xi . 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

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Other contributions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Author: Bergman, Jakob
Holmquist, B.
Date: 2011 May 12
Abstract: Cleveland (1979) is usually credited with the introduction of the locally weighted regression, Loess. The concept was further developed by Cleveland and Devlin (1988). The general idea is that for an arbitrary number of explanatory data points xi the value of a dependent variable is estimated ˆyi . The ˆyi is the fitted value from a dth degree polynomial in xi . (In practice often d = 1.) The ˆyi is fitted using weighted least squares, WLS, where the points xk (k = 1, . . . , n) closest to xi are given the largest weights. 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 xi we for each xi fit a dth degree polynomial in xi yielding an estimate ˆyi of the composition yi . We use C-WLS to fit the polynomial giving the largest weights to the points xk (k = 1, . . . , n) closest to xi . 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
Format: application/pdf
Document access: http://hdl.handle.net/10256/13633
Language: eng
Publisher: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Collection: CoDaWork 2011. The 4th International Workshop on Compositional Data Analysis
Rights: Tots els drets reservats
Subject: Estadística matemàtica -- Congressos
Mathematical statistics -- Congresses
Anàlisi multivariable -- Congressos
Multivariate analysis -- Congresses
Title: Compositional Loess Modelling
Type: info:eu-repo/semantics/conferenceObject
Repository: DUGiDocs

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