Prediction Intervals in Partial Least Squares Regression via a New Local Linearization Approach Articles uri icon

publication date

  • October 2010

start page

  • 122

end page

  • 128


  • 2


  • 103

International Standard Serial Number (ISSN)

  • 0169-7439

Electronic International Standard Serial Number (EISSN)

  • 1873-3239


  • Univariate Partial Least Squares is a biased regression procedure for calibration and prediction widely used in chemometrics. To the best of our knowledge the distributional properties of the PLS regression
    estimator still remain unpublished and this leads to difficulties in
    performing inference-based procedures such as obtaining prediction
    intervals for new samples. Prediction intervals require the variance of
    the regression estimator to be known in order to evaluate the variance
    of the prediction. Because the nonlinearity of the regression estimator
    on the response variable, local linear approximation through the
    delta-method for the PLS regression vector have been proposed in the
    literature. In this paper we present a different local linearization
    which is carried out around the vector of the covariances between
    response and predictors, and covariances between predictors. This
    approach improves the previous ones in terms of bias and precision.
    Moreover, the proposed algorithm speeds up the calculations of the
    Jacobian matrix and performs better than recent efficient