Modelling and forecasting with robust canonical analysis: Method and application

Asher Tishler, Stan Lipovetsky

Research output: Contribution to journalArticlepeer-review

Abstract

Multivariate methods often serve as an intelligent way to study the relations between two data sets. When the number of variables in one or both data sets is large, which is usually the case, the correlation matrices of the data sets may be singular or ill-conditioned. When this happens the weights obtained by multivariate methods that require the inversion of the correlation matrices are not unique, or highly unreliable. Here we present and apply a robust estimation and forecasting method that does not require us to invert the correlation matrices. This method, which we call robust canonical analysis (RCA), is a straightforward extension of the simple covariance of two variables to two data sets. As an example we use the RCA method to estimate the relations between a set of measures that describe how the firm manages its relations with its customers, and a set of variables that describe the utility of information systems applications to the firm's operations. Scope and purpose Researchers often employ multivariate analysis when they need to represent a very large data set by several easy-to-interpret variables, or when it is necessary to relate one set of variables to another. These methods facilitate identification of effects of key variables of one data set on all or several of the variables in the other data set. Thus, they can also be used as data reduction methods. Depending on the particular application and the available data, a multivariate method serves either as the first stage of the quantitative analysis, or as the true representation of the theoretical model. In this study we present a multivariate generalization of covariance as a first-order approximation to the true relations between two large data sets that may exhibit severe multicollinearity among the variables.

Original languageEnglish
Pages (from-to)217-232
Number of pages16
JournalComputers and Operations Research
Volume27
Issue number3
DOIs
StatePublished - Mar 2000

Keywords

  • Canonical correlation
  • Eigenvector analysis
  • Robust canonical analysis

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