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Regression methods in multidimensional prediction and estimation
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
2007 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

In regression with near collinear explanatory variables, the least squares predictor has large variance. Ordinary least squares regression (OLSR) often leads to unrealistic regression coefficients. Several regularized regression methods have been proposed as alternatives. Well-known are principal components regression (PCR), ridge regression (RR) and continuum regression (CR). The latter two involve a continuous metaparameter, offering additional flexibility.

For a univariate response variable, CR incorporates OLSR, PLSR, and PCR as special cases, for special values of the metaparameter. CR is also closely related to RR. However, CR can in fact yield regressors that vary discontinuously with the metaparameter. Thus, the relation between CR and RR is not always one-to-one. We develop a new class of regression methods, LSRR, essentially the same as CR, but without discontinuities, and prove that any optimization principle will yield a regressor proportional to a RR, provided only that the principle implies maximizing some function of the regressor's sample correlation coefficient and its sample variance. For a multivariate response vector we demonstrate that a number of well-established regression methods are related, in that they are special cases of basically one general procedure. We try a more general method based on this procedure, with two meta-parameters. In a simulation study we compare this method to ridge regression, multivariate PLSR and repeated univariate PLSR. For most types of data studied, all methods do approximately equally well. There are cases where RR and LSRR yield larger errors than the other methods, and we conclude that one-factor methods are not adequate for situations where more than one latent variable are needed to describe the data. Among those based on latent variables, none of the methods tried is superior to the others in any obvious way.

sted, utgiver, år, opplag, sider
Stockholm: Matematiska institutionen , 2007. , s. 146
Emneord [en]
regression, prediction, principal compnents regression, ridge regression, partial least squares
HSV kategori
Forskningsprogram
matematisk statistik
Identifikatorer
URN: urn:nbn:se:su:diva-7025ISBN: 978-91-7155-486-4 (tryckt)OAI: oai:DiVA.org:su-7025DiVA, id: diva2:197492
Disputas
2007-09-28, sal 14, hus 5, Kräftriket, Stockholm, 13:00
Opponent
Veileder
Tilgjengelig fra: 2007-09-06 Laget: 2007-08-28bibliografisk kontrollert
Delarbeid
1. Continuum regression is not always continuous
Åpne denne publikasjonen i ny fane eller vindu >>Continuum regression is not always continuous
1996 Inngår i: J. R. Statist. Soc., Vol. B 58, nr 4, s. 703-710Artikkel i tidsskrift (Fagfellevurdert) Published
Identifikatorer
urn:nbn:se:su:diva-24415 (URN)
Merknad
Part of urn:nbn:se:su:diva-7025Tilgjengelig fra: 2007-09-06 Laget: 2007-08-28bibliografisk kontrollert
2. A Generalized View on Continuum Regression
Åpne denne publikasjonen i ny fane eller vindu >>A Generalized View on Continuum Regression
1999 Inngår i: Scand. J. Statist., ISSN 0303-6898, Vol. 26, nr 1, s. 17-30Artikkel i tidsskrift (Fagfellevurdert) Published
Identifikatorer
urn:nbn:se:su:diva-24416 (URN)
Merknad
Part of urn:nbn:se:su:diva-7025Tilgjengelig fra: 2007-09-06 Laget: 2007-08-28bibliografisk kontrollert
3. Ridge Regression and inverse problems
Åpne denne publikasjonen i ny fane eller vindu >>Ridge Regression and inverse problems
Manuskript (Annet vitenskapelig)
Identifikatorer
urn:nbn:se:su:diva-24417 (URN)
Merknad
Part of urn:nbn:se:su:diva-7025Tilgjengelig fra: 2007-09-06 Laget: 2007-08-28 Sist oppdatert: 2010-01-13bibliografisk kontrollert
4. A two-parametric class of predictors in multivariate regression
Åpne denne publikasjonen i ny fane eller vindu >>A two-parametric class of predictors in multivariate regression
2007 (engelsk)Inngår i: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 21, nr 5-6, s. 215-226Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We demonstrate that a number of well-established multivariate regression methods for prediction are related in that they are special cases of basically one general procedure. We try a more general method based on this procedure with two metaparameters. In a simulation study, based on a latent structure model, we compare this method to ridge regression (RR), multivariate partial least squares regression (PLSR) and repeated univariate PLSR. For most types of data sets studied, all methods do approximately equally well. There are some cases where RR and least squares ridge regression (LSRR) yield larger errors than the other methods, and we conclude that one-factor methods are not adequate for situations where more than one latent variable are needed to describe the data. Among those based on latent variables, none of the methods tried is superior to the others in any obvious way.

Emneord
joint continuum regression, multivariate prediction, multivariate regression, PCR, PLSR, reduced rank regression, ridge regression, SIMPLS, total least squares
HSV kategori
Identifikatorer
urn:nbn:se:su:diva-24418 (URN)10.1002/cem.1063 (DOI)000250098200006 ()
Merknad
Part of urn:nbn:se:su:diva-7025Tilgjengelig fra: 2007-09-06 Laget: 2007-08-28 Sist oppdatert: 2019-12-17bibliografisk kontrollert
5. Krylov sequences as a tool for analysing iterated regression algorithms
Åpne denne publikasjonen i ny fane eller vindu >>Krylov sequences as a tool for analysing iterated regression algorithms
Manuskript (Annet vitenskapelig)
Identifikatorer
urn:nbn:se:su:diva-24419 (URN)
Merknad
Part of urn:nbn:se:su:diva-7025Tilgjengelig fra: 2007-09-06 Laget: 2007-08-28 Sist oppdatert: 2010-01-13bibliografisk kontrollert

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