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Maximum Likelihood Estimators in a Two Step Model for PLS
Swedish University of Agriculture Science, Sweden .
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
2012 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, no 13-14, 2503-2511 p.Article in journal (Refereed) Published
Abstract [en]

Univariate partial least squares regression (PLS1) is a method of modeling relationships between a response variable and explanatory variables, especially when the explanatory variables are almost collinear. The purpose is to predict a future response observation, although in many applications there is an interest to understand the contributions of each explanatory variable. It is an algorithmic approach. In this article, we are going to use the algorithm presented by Helland (1988). The population PLS predictor is linked to a linear model including a Krylov design matrix and a two-step estimation procedure. For the first step, the maximum likelihood approach is applied to a specific multivariate linear model, generating tools for evaluating the information in the explanatory variables. It is shown that explicit maximum likelihood estimators of the dispersion matrix can be obtained where the dispersion matrix, besides representing the variation in the error, also includes the Krylov structured design matrix describing the mean.

Place, publisher, year, edition, pages
Taylor andamp; Francis: STM, Behavioural Science and Public Health Titles / Taylor andamp; Francis , 2012. Vol. 41, no 13-14, 2503-2511 p.
Keyword [en]
Krylov design; Krylov sequence; Krylov space; Maximum likelihood estimators; PLS; Variance estimator
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-79841DOI: 10.1080/03610926.2011.607531ISI: 000305208600018OAI: diva2:544376
Available from: 2012-08-14 Created: 2012-08-14 Last updated: 2012-08-14

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von Rosen, Dietrich
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Mathematical Statistics The Institute of Technology
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