Some theoretical aspects of partial least squares regression

By Inge S. Helland. 2001

213 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9b78873c819f97fc4a7218dec9b328918e5a1bc6

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In Analytical Chemistry

In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Partial least squares prediction in high-dimensional regression (2019, background): “Helland [21] was perhaps the first to define a PLS regression model, and a first attempt at maximum likelihood estimation was made by Helland [22]; see also [23, 29].”
A comparison of model-based and regression classification techniques applied to near infrared spectroscopic data in food authentication studies (2007, methodology): “so that if m = 0 no correlation between X and y exists and m = p is the full least squares model; this agrees with [ 18 ].”
Partial Least Squares (2005, methodology): “Project the score ta: xa ¼ xa 1 tapa The output of PLS after a steps is ŷ ¼ yþ Pa j¼1 qjtj, which can equivalently be written as ŷ ¼ yþ ra ðx xÞ As derived in References [6,24], this version of PLS is defined in a population setting with an infinite amount of data points so that expectations are o”
Overview and Recent Advances in Partial Least Squares (2005, methodology): “PLS regression used to be overlooked by statisticians and is still considered rather an algorithm than a rigorous statistical model [14].”
A review of variable selection methods in Partial Least Squares Regression (2012, background): “Many authors, for example [1–5], have addressed this problem and there are numerous suggested approaches for dealing with the so-called large p small n problem [1], that is, many variables and few samples.”
The prediction error in CLS and PLS: the importance of feature selection prior to multivariate calibration (2005, methodology): “Wentzell and Vega-Montoto [ 10 ] also made an extensive numerical comparison of PLS and PCR with simulated data containing many components.”
Envelopes and partial least squares regression (2013, methodology): “This population model was further discussed by Næs and Helland (1993) and by Helland (2001), and a first attempt at maximum likelihood estimation was given by Helland (1992).”