In this short note, we derive an expression for the asymptotic covariance matrix of the univariate partial least squares (PLS) estimator. In contrast to M.C. Denham [J. Chemometrics 11 (1997) 39], who provided a locally linear approximation based on a recursive definition of the estimator, we derive a more compact expression for the asymptotic covariance matrix by combining a standard convergence result with matrix differential calculus, in particular the approach of J.R. Magnus and H. Neudecker [Matrix Differential Calculus with Applications in Statistics and Econometrics, revised ed., Wiley, Chichester, UK, 1991]. We also describe some theoretical and practical aspects of calculating the asymptotic covariance matrix, and illustrate its use on spectroscopic data.
Phatak, A., Reilly, P. M., & Penlidis, A. (2002). The asymptotic variance of the univariate PLS estimator. Linear Algebra and Its Applications, 354(1–3), 245–253. https://doi.org/10.1016/S0024-3795(01)00357-3