Effective rank for multivariate calibration methods

Journal of Chemometrics

Volumn 18, Issue 6, 2004, Pages 306-311

  Seipel, Heather A ^a   Kalivas, John H ^a  

^a IDAHO STATE UNIVERSITY   (United States)

Author keywords

Calibration; Degrees of freedom; Effective rank; Parsimony; Prediction rank; Rank

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); LEAST SQUARES APPROXIMATIONS; PRINCIPAL COMPONENT ANALYSIS; REGRESSION ANALYSIS;

DATA SET; DEGREE OF FREEDOM; EFFECTIVE RANK; MODEL METHOD; MULTIVARIATE CALIBRATION METHODS; PARSIMONY; PREDICTION RANK; PRINCIPAL COMPONENTS; RANK; RIDGE REGRESSION;

FORECASTING;

ANALYTIC METHOD; ARTICLE; CALIBRATION; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MULTIVARIATE ANALYSIS; PARSIMONY ANALYSIS; PRINCIPAL COMPONENT ANALYSIS; REGRESSION ANALYSIS; STATISTICS;

EID: 9444271627     PISSN: 08869383     EISSN: None     Source Type: Journal    
DOI: 10.1002/cem.874     Document Type: Article

References (19)

1. Kalivas JH, Green RL. Pareto optimal multivariate calibration for spectroscopic data. Appl. Spectrosc. 2001; 55: 1645-1652.
2. Kalivas JH. Basis sets for multivariate regression. Anal. Chim. Acta 2001; 428: 31-40.
3. Kalivas JH. Interrelationships of multivariate regression methods using eigenvector basis sets. J. Chemometrics 1999; 13: 111-132.
4. Hansen PC. Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion. SIAM: Philadelphia, PA, 1991.
5. Gilliam DS, Lund JR, Vogel CR. Quantifying information content for ill-posed problems. Inverse Problems. 1990; 6: 725-736.
6. Myers RH. Classical and Modern Regression with Applications. PWS-Kent-Publishing: Boston, MA, 1990.
7. Manne R. Analysis of two partial-least-squares algorithms for multivariate calibration. Chemometrics Intell. Lab. Syst. 1987; 2: 187-197.
8. Phatak A, De Hoog F. Exploiting the connection between PLS, Lanczos methods and conjugate gradients: alternative proofs of some properties of PLS. J. Chemometrics 2002; 16: 361-367.
9. Van der Voet H. Pseudo-degrees of freedom for complex predictive models: the example of partial least squares. J. Chemometrics 1999; 13: 195-208.
10. Shao J. Linear model selection by cross-validation. J. Am. Statist. Assoc. 1993; 88: 486-494.
11. Baumann K. Cross-validation as the objective function for variable-selection techniques. Trends Anal. Chem. 2003; 22: 395-406.
12. Wise BM, Gallagher NB, Bro R, Shaver JM. PLS_Toolbox 3.0 for Use with MATLAB. Eigenvector Research: Manson, WA, 2003.
13. Fearn T. A misuse of ridge regression in the calibration of a near infrared reflectance instrument. Appl. Statist. 1983; 32: 73-79.
14. Kalivas JH. Two data sets of near infrared spectra. Chemometrics Intell. Lab. Syst. 1997; 37: 255-259.
15. Anderson KJ, Kalivas JH. Assessment of pareto calibration, stability, and wavelength selection. Appl. Spectrosc. 2003; 57: 309-316.
16. Lawson CL, Hanson RJ. Solving Least Squares Problems. Prentice-Hall: Englewood Cliffs, NJ, 1974.
17. Hansen PC, O'Leary DP. The use of the L-curve in the regularization of discrete ill-posed problems. J. Sci. Comput. 1993; 14: 1487-1503.
18. Ye J. On measuring and correcting the effects of data mining and model selection. J. Am. Stat. Assoc. 1998; 93: 120-131.
19. Forrest JB, Kalivas JH. Ridge regression using a harmonious approach. Submitted to J. Chemometrics.