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Model Reduction for Prediction in Regression Models

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  • Inge S. Helland

Abstract

We look at prediction in regression models under squared loss for the random x case with many explanatory variables. Model reduction is done by conditioning upon only a small number of linear combinations of the original variables. The corresponding reduced model will then essentially be the population model for the chemometricians' partial least squares algorithm. Estimation of the selection matrix under this model is briefly discussed, and analoguous results for the case with multivariate response are formulated. Finally, it is shown that an assumption of multinormality may be weakened to assuming elliptically symmetric distribution, and that some of the results are valid without any distributional assumption at all.

Suggested Citation

  • Inge S. Helland, 2000. "Model Reduction for Prediction in Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 1-20, March.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:1:p:1-20
    DOI: 10.1111/1467-9469.00174
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    Cited by:

    1. Wenyang Zhang & Qiwei Yao & Howell Tong & Nils Chr. Stenseth, 2003. "Smoothing for Spatiotemporal Models and Its Application to Modeling Muskrat-Mink Interaction," Biometrics, The International Biometric Society, vol. 59(4), pages 813-821, December.
    2. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.

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