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A Note on the Dimension of the Projection Space in a Latent Factor Regression Model with Application to Business Cycle Classification

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  • Weihs, Claus
  • Luebke, Karsten

Abstract

In this paper it is shown that the number of latent factors in a multiple multivariate regression model need not be larger than the number of the response variables in order to achieve an optimal prediction. The practical importance of this lemma is outlined and an application of such a projection on latent factors in a classification example is given.

Suggested Citation

  • Weihs, Claus & Luebke, Karsten, 2004. "A Note on the Dimension of the Projection Space in a Latent Factor Regression Model with Application to Business Cycle Classification," Technical Reports 2004,29, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200429
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    File URL: https://www.econstor.eu/bitstream/10419/22541/1/tr29-04.pdf
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    References listed on IDEAS

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    1. Weihs, Claus & Garczarek, Ursula, 2002. "Stability of multivariate representation of business cycles over time," Technical Reports 2002,20, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Weihs, Claus & Hothorn, Torsten, 2002. "Determination of optimal prediction oriented multivariate latent factor models using loss functions," Technical Reports 2002,15, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Groß, Jürgen & Lübke, Karsten & Weihs, Claus, 2002. "A note on the general solution for a projection matrix in latent factor models," Technical Reports 2002,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Citations

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    Cited by:

    1. Luebke, Karsten & Czogiel, Irina & Weihs, Claus, 2004. "Latent Factor Prediction Pursuit for Rank Deficient Regressors," Technical Reports 2004,75, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Weihs, Claus & Luebke, Karsten, 2005. "Prediction Optimal Classification of Business Phases," Technical Reports 2005,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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    1. Luebke, Karsten & Weihs, Claus, 2004. "Generation of prediction optimal projection on latent factors by a stochastic search algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 297-310, September.
    2. Luebke, Karsten & Czogiel, Irina & Weihs, Claus, 2004. "Latent Factor Prediction Pursuit for Rank Deficient Regressors," Technical Reports 2004,75, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Enache, Daniel & Weihs, Claus, 2004. "Importance Assessment of Correlated Predictors in Business Cycles Classification," Technical Reports 2004,66, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Pumplün, Constanze & Weihs, Claus & Preusser, Andrea, 2004. "Experimental Design for Variable Selection in data bases," Technical Reports 2004,72, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Garczarek, Ursula & Weihs, Claus & Enache, Daniel, 2005. "Classification-relevant Importance Measures for the West German Business Cycle," Technical Reports 2005,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Weihs, Claus & Luebke, Karsten, 2005. "Prediction Optimal Classification of Business Phases," Technical Reports 2005,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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