The Mahalanobis distance

Mahalanobis, 1936, On the generalised distance in statistics, Proceedings of the National Institute of Science of India, 12, 49

H. Martens, T. Naes, Multivariate Calibration, Wiley, Chichester, 1991.

P.J. Rousseeuw, A.M. Leroy, Robust Regression and Outlier Detection, Wiley, New York, 1987.

Shenk, 1991, Population definition, sample selection, and calibration procedures for near-infrared reflectance spectroscopy, Crop Science, 31, 469, 10.2135/cropsci1991.0011183X003100020049x

Jouan-Rimbaud, 1997, Characterisation of the representativity of selected sets of samples in multivariate calibration and pattern recognition, Anal. Chim. Acta, 350, 149, 10.1016/S0003-2670(97)00296-1

Jouan-Rimbaud, 1998, Determination of the representativity between two multidimensional data sets by a comparison of their structure, Chemom. Intell. Lab. Syst., 40, 129, 10.1016/S0169-7439(98)00005-7

H. Hotelling, Analysis of a complex of statistical variables into principal components, J. Educ. Psychol. 24 (1933) 417-441, 498–520.

H. Hotelling, Multivariate quality control, in: C. Eisenhart, M.W. Hastay, W.A. Wallis (Eds.), Techniques of Statistical Analysis, McGraw-Hill, New York, 1947, pp. 111–184.

B.M.G. Vandeginste, D.L. Massart, L.M.C. Buydens, S. De Jong, P.J. Lewi, J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics: Part B, Elsevier, Amsterdam, 1998.

Wu, 1996, Comparison of regularised discriminant analysis, linear discriminant analysis and quadratic discriminant analysis, applied to NIR data, Anal. Chim. Acta, 329, 257, 10.1016/0003-2670(96)00142-0

Derde, 1986, UNEQ: a disjoint modelling technique for pattern recognition based on normal distribution, Anal. Chim. Acta, 184, 33, 10.1016/S0003-2670(00)86468-5

Coomans, 1984, Use of a microcomputer for the definition of multivariate confidence regions in medical diagnosis bases on clinical laboratory profiles, Comp. Biomed. Res., 17, 1, 10.1016/0010-4809(84)90002-8

Wold, 1977, SIMCA: a method for analysing chemical data in terms of similarity and analogy, ACS Symposium Series, 52, 10.1021/bk-1977-0052.ch012

G. Box, A. Luceno, Statistical Control by Monitoring and Feedback Adjustment, Wiley, New York, 1997.

P. Dagnelie, Statistique Théoretique et Appliquée Tome 1, Les Presses agronomiques de Gembloux, 1992.

A.C. Rencher, Multivariate Statistical Interference and Applications, Wiley, New York, 1998.

J.E. Jackson, A User's Guide To Principal Components, Wiley, New York, 1991.

F. Malinowski, D. Howery, Factor Analysis in Chemistry, Wiley, New York, 1980.

Grubbs, 1972, Extension of sample sizes and percentage points for significance tests of outlying observations, Technometrics, 14, 847, 10.2307/1267134

Kelly, 1990, Outlier detection in collaborative studies, J. Assoc. Off. Anal. Chem., 73, 58

Centner, 1996, Detection of inhomogeneities in sets of NIR spectra, Anal. Chim. Acta, 330, 1, 10.1016/0003-2670(96)00150-X

J.C. Miller, J.N. Miller, Statistics for Analytical Chemistry, Ellis Horwood, Chichester, 1988.

P. Dagnelie, Analyse Statistique a Plusieurs Variables, Vander, Paris, 1975.

Tracy, 1992, Multivariate control charts for individual observations, J. Qual. Technol., 24, 88, 10.1080/00224065.1992.12015232

Jackson, 1980, Principal components and factor analysis: Part I. Principal components, J. Qual. Technol., 12, 201, 10.1080/00224065.1980.11980967

Jackson, 1981, Principal components and factor analysis: Part II. Additional topics related to principal components, J. Qual. Technol., 13, 46, 10.1080/00224065.1981.11980986

MacGregor, 1995, Statistical process control of multivariate processes, Control Eng. Practice, 3, 403, 10.1016/0967-0661(95)00014-L

Næs, 1989, Leverage and influence measures for principal component regression, Chemom. Intell. Lab. Syst., 5, 155, 10.1016/0169-7439(89)80012-7

D.L. Massart, B.M.G. Vandeginste, L.M.C. Buydens, S. De Jong, P.J. Lewi, J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics: Part A, Elsevier, Amsterdam, 1997.

I.E. Frank, R. Todeschini, The Data Analysis Handbook, Elsevier, Amsterdam, 1994.

Rousseeuw, 1983, Multivariate estimation with high breakdown point, Inst. Math. Stat. Bull., 12, 234

Rousseeuw, 1997, Introduction to positive breakdown methods, Handbook of Statistics, 15, 101, 10.1016/S0169-7161(97)15007-6

Jackson, 1959, Quality control methods for several related variables, Technometrics, 1, 359, 10.2307/1266717

Montgomery, 1972, Economic design of T2 control charts to maintain current control of a process, Management Science, 19, 76, 10.1287/mnsc.19.1.76

F.B. Alt, Multivariate quality control, in: S. Kotz, N.L. Johnson (Eds.), Encyclopedia of Statistical Sciences, Vol. 6, Wiley, New York, 1985, pp. 110–122.

T.P. Ryan, Statistical Methods for Quality Improvement, Wiley, New York, 1988.

Fuchs, 1994, Multivariate profile charts for statistical process control, Technometrics, 36, 182, 10.2307/1270230

Wold, 1978, Cross-validatory estimation of the number of components in factor and principal components models, Technometrics, 20, 397, 10.2307/1267639

Kourti, 1995, Process analysis, monitoring and diagnosis, using multivariate projection methods, Chemom. Intell. Lab. Syst., 28, 3, 10.1016/0169-7439(95)80036-9

Dagnelie, 1991, Using generalised distances in classification of groups, Biom. J., 33, 683, 10.1002/bimj.4710330607

P.A. Lachenbruch, Discriminant Analysis, Hafner Press, New York, 1975.

Friedman, 1989, Regularized discriminant analysis, J. Am. Stat. Assoc., 84, 165, 10.2307/2289860

Aeberhard, 1993, Improvements to the classification performance of RDA, J. Chemom., 7, 99, 10.1002/cem.1180070204

Mertens, 1994, Principal component outlier detection and SIMCA: a synthesis, Analyst, 119, 2777, 10.1039/an9941902777

Wold, 1987, Letter to the editor — Comments on a recent evaluation of the SIMCA method, J. Chemom., 1, 243, 10.1002/cem.1180010406

De Maesschalck, 1999, Decision criteria for SIMCA applied to near infrared data, Chemom. Intell. Lab. Syst., 47, 63, 10.1016/S0169-7439(98)00159-2

Smith, 1991, Composite multivariate quality control using a system of univariate, bivariate, and multivariate quality control rules, Anal. Chem., 63, 1419, 10.1021/ac00014a015

Caudill, 1992, Performance characteristics of a composite multivariate quality control system, Anal. Chem., 64, 1390, 10.1021/ac00037a016

Kourti, 1995, Process analysis, monitoring and diagnosis, using multivariate projection methods, Chemom. Intell. Lab. Syst., 28, 3, 10.1016/0169-7439(95)80036-9

Nomikos, 1995, Multivariate SPC charts for monitoring Bach processes, Technometrics, 37, 41, 10.2307/1269152

MacGregor, 1995, Statistical process control of multivariate processes, Control Eng. Practice, 3, 403, 10.1016/0967-0661(95)00014-L

De Maesschalck, 1998, On-line monitoring of powder blending with near-infrared spectroscopy, Appl. Spectrosc., 52, 725, 10.1366/0003702981944148

Nijhuis, 1997, Multivariate statistical process control in chromatography, Chemom. Intell. Lab. Syst., 38, 51, 10.1016/S0169-7439(97)00054-3

Cho, 1995, Pattern recognition analysis of near-infrared spectra by Robust distance method, J. Chemom., 9, 169, 10.1002/cem.1180090304

Coomans, 1984, Use of a microcomputer for the definition of multivariate confidence regions in medical diagnosis bases on clinical laboratory profiles, Comp. Biomed. Res., 17, 1, 10.1016/0010-4809(84)90002-8

Derde, 1986, UNEQ: a disjoint modelling technique for pattern recognition based on normal distribution, Anal. Chim. Acta, 184, 33, 10.1016/S0003-2670(00)86468-5

Mark, 1987, Use of Mahalanobis distances to evaluate sample preparation methods for near-infrared reflectance analysis, Anal. Chem., 59, 790, 10.1021/ac00132a024

Gemperline, 1995, Classification of near-infrared spectra using wavelength distances: comparison to the Mahalanobis distance and residual variance methods, Anal. Chem., 67, 160, 10.1021/ac00097a025

Mark, 1985, Qualitative near-infrared reflectance analysis using Mahalanobis distances, Anal. Chem., 57, 1449, 10.1021/ac00284a061

Aldridge, 1996, Near-IR detection of polymorphism and process-related substances, Anal. Chem., 68, 997, 10.1021/ac950993x

Martin, 1996, Application of pattern recognition to the discrimination of roasted coffees, Anal. Chim. Acta, 320, 191, 10.1016/0003-2670(95)00550-1

Martin, 1999, Classification of vegetable oils by linear discriminant analysis of Electronic Nose data, Anal. Chim. Acta, 384, 83, 10.1016/S0003-2670(98)00851-4

Lee, 1998, Characterisation of fatty acids composition in vegetable oils by gas chromatography and chemometrics, Anal. Chim. Acta, 358, 163, 10.1016/S0003-2670(97)00574-6

Ramadan, 1998, Classification of detectors for ion chromatography using principal components regression and linear discriminant analysis, Chemom. Intell. Lab. Syst., 40, 165, 10.1016/S0169-7439(98)00020-3