Abstract
Partial LAD regression uses the L 1 norm associated with least absolute deviations (LAD) regression while retaining the same algorithmic structure of univariate partial least squares (PLS) regression. We use the bootstrap in order to assess the partial LAD regression model performance and to make comparisons to PLS regression. We use a variety of examples coming from NIR experiments as well as two sets of experimental data.
Similar content being viewed by others
References
Denham M (2000). Choosing the number of factors in partial least squares regression: estimating and minimizing the mean squared error of prediction. J Chemom 14:351–361
Diaconis P, Efron B (1983). Computer-intensive methods in statistics. Sci Am 248:116–130
Dodge Y, Kondylis A, Whittaker J (2004). Extending PLS to PLAD regression and the use of the L1 norm in soft modelling. In: Antoch J (ed) Proceedings in computational statistics, COMPSTAT’04. Physica-Verlag/Springer, Heidelberg, pp 935–942
Edgington ES (1995). Randomization tests. Marcel Dekker, New York
Efron B, Gong G (1983). A leisurely look at the bootstrap, the jackknife, and cross-validation. Am Stat 37:36–48
Efron B (1987). Better bootstrap confidence intervals. J Am Stat Assoc 82:171–185
Efron B, Tibshirani R (1993). An introduction to the bootstrap. Chapman and Hall, New York
Efron B, Tibshirani R (1997). Improvements on cross-validation: the .632+ bootstrap method. J Am Stat Assoc 92:548–560
Fearn T (1983). A Missue of ridge regression in the calibration of a near infrared reflectance instrument. Appl Stat 32:73–79
Gnanadesikan R, Kettenring JR (1972). Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics 28:81–124
Huber PJ (1981). Robust statistics. Wiley, New York
Kondylis A, Whittaker J (2005). Using the bootstrap on PLAD regression. In: Aluja T, Casanovas J, Vinzi VE, Morineau A, Tenehaus M (eds) PLS and related methods. Proceedings of the PLS’05 international symposium, Barcelona, pp 395–402
Martens H, Naes T (1989). Multivariate calibration. Wiley, UK
Naes T (1985). Multivariate calibration when the error covariance matrix is structured. Technometrics 27:301–311
Shao J (1993). Linear model selection by cross-validation. J Am Stat Assoc 88:486–494
Tenenhaus M (1998). La régression PLS. Théorie et pratique. Technip, Paris
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kondylis, A., Whittaker, J. An empirical study of PLAD regression using the bootstrap. Computational Statistics 22, 307–321 (2007). https://doi.org/10.1007/s00180-007-0034-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00180-007-0034-3