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The price paid for the second‐order advantage when using the generalized rank annihilation method (GRAM)
Author(s) -
Faber Nicolaas Klaas M.
Publication year - 2001
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.688
Subject(s) - chemometrics , rank (graph theory) , calibration , bilinear interpolation , variance (accounting) , mathematics , gram , least squares function approximation , computer science , statistics , algorithm , machine learning , combinatorics , bacteria , accounting , estimator , biology , business , genetics
In a ground‐breaking paper, Linder and Sundberg developed a statistical framework for the calibration of bilinear data ( Chemometrics Intell. Lab. Syst . 1998; 42 : 159–178). Within this framework they formulated three different predictor construction methods ( J. Chemometrics accepted), namely a so‐called naive method, a least squares (LS) method and a refined version of the latter that takes account of the calibration uncertainty. They showed that the naive method is statistically less efficient than the others under the assumption of white noise. In the current work a close relationship is established between the generalized rank annihilation method (GRAM) and the naive method by comparing expressions for prediction variance. The main conclusion is that the relatively poor efficiency of GRAM is the price one pays for obtaining the second‐order advantage with a single calibration sample. Copyright © 2001 John Wiley & Sons, Ltd.