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Operator related to a data matrix: a survey. (English) Zbl 1437.62019
Rizzi, Alfredo (ed.) et al., COMPSTAT. Proceedings in computational statistics. 17th symposium held in Rome, Italy, August 28 – September 1, 2006. With CD-Rom. Heidelberg: Physica-Verlag. 285-297 (2006).
Summary: The reading of this article will allow the readers to understand the data analysis approach which is proposed. The first paragraph gives the basic tools: the triplet (X, Q, D), the operator related to a data matrix and the coefficient RV. The two following paragraphs show how these tools are used for reading out and solving the problems of joint analysis of several data matrices and of principal component analysis with respect to instrumental variables. The conclusion recalls of the construction of this approach along the past thirty five years.
For the entire collection see [Zbl 1097.62502].
MSC:
62-08 Computational methods for problems pertaining to statistics
62H25 Factor analysis and principal components; correspondence analysis
Software:
ade4
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References:
[1] Beh E.J (1997) Simple correspondence analysis of ordinal cross-clasifications using orthogonal polynolials. Biometrical Journal 39, 589-613 · Zbl 1127.62370
[2] Bonifas L, Escoufier Y, Gonzalez P.L, Sabatier R (1984) Choix de variables en analyse en composantes principales. Rev. Statistique Appliquée XXXII(2) 5-15 · Zbl 0583.62053
[3] Caillez F, Pages J.P (1976) Introduction á l’analyse des données SMASH, Paris
[4] Chessel D, Dufour A.B, Thioulouse J (2004) The ade4 package — I: One-table methods. R News 4: 5-10
[5] Cléroux R, Ducharme G (1989) Vector correlation for elliptical distribution. Comm. Stat. A, 18, 1441-1454. · Zbl 0696.62246
[6] Cléroux R, Lazraq A, Lepage Y (1995) Vector correlation based on ranks and a nonparametric test of no association between vectors. Communications in Stat., 24, 713-733. · Zbl 0825.62304
[7] D’Ambra L, Beh E.J, Amenta P (2005) Catanova for two — way contingency tables with ordinal variables using orthogonal polynomials. Communications in statistics, theory and methods, 34, 1755-1770. · Zbl 1075.62057
[8] Durand J.F (1992) Additive spline discriminant analysis. In: Y. Dodge and J.C. Whittakers (eds) Computational Statistics, Heidelberg: Physica — Verlag, I, 145-150.
[9] Durand J.F (1993) Generalized principal component analysis with respect to instrumental variables via univariate spline transformations. Computational Statistics and Data Analysis, 16, 423-440. · Zbl 0937.62604
[10] Escoufier Y (1970) Echantillonnage dans une population de variables aléatoires réelles. Publl. Inst.Statist. Univ. Paris 19,4, 1-47. · Zbl 0264.62021
[11] Escoufier Y (1973) Le traitement des variables vectorielles. Biometrics 29, 751-760.
[12] Escoufier Y (1977) Operators related to a data matrix. In: J.R. Barra (ed) Recents developpements in Statistics: North — Holland Publishing Company, 125-131. · Zbl 0367.62078
[13] Escoufier Y (1980) Exploratory data analysis when data are matrices. In: K. Matusita (ed) Recent developments in Statistical inference and data analysis: North — Holland Publishing Company · Zbl 0462.62004
[14] Escoufier Y (1986) A propos du choix de variables en analyse des données. Metron XLIV, 31-47. · Zbl 0621.62060
[15] Escoufier Y (1987) The duality diagramm: a means of better practical applications. In: Legendre P. and Legendre L (eds) Development in numerical ecology, Nato ASI series, Vol.G14, Springer — Verlag, Berlin Heidelberg, 139-156.
[16] Escoufier Y, L’Hermier H (1978) A propos de la comparaison graphique des matrices de variance. Biom.J. vol.20, 477-483. · Zbl 0388.62065
[17] Escoufier Y, Robert P (1979) Choosing variables and metrics by optimizing the RV — coefficient. In: Optimizing methods in Statistics: Academic Press, Inc. · Zbl 0473.62002
[18] Escoufier Y, Robert P, Cambon J (1974) Construction of a vector equivalent to a given vector from the point of view of the analysis of principal components: Compstat, Vienne.
[19] Fraile L, Escoufier Y, Raibaut A (1993) Analyse des correspondances de données planifiées: étude de la chémotaxie de la larve infestante d’un parasite. Biometrics 49, 1142-1153.
[20] Holmes S (2006) Multivariate Statistics: The French Way In: D. Nolan and T. Speed (eds) Festschrift for David Freedman, IMS Lectures Notes — Monograph Series, Ohio. To appear.
[21] Iman W, Abdelkbir S, Escoufier Y (1998) Quantification des effets spatiaux linéaires et non linéaires dans l’explication d’un tableau de données concernant la qualité des eaux souterraines. Rev. Statistique Appliquée, XLVI(3) 37-52.
[22] Lavit Ch (1988) Analyse conjointe des tableaux quantitatifs: Masson, Paris
[23] Lavit Ch, Escoufier Y, Sabatier R, Traissac P (1994) The ACT ( STATIS method). Computational Statistics & Data Analysis 18, 97-119. · Zbl 0825.62009
[24] Kazi-Aoual F, Hitier S, Sabatier R, Lebreton J.D (1995) Refined approximations to permutation tests for multivariate inference. Computational Statistics & Data Analysis 20, 643-656. · Zbl 0875.62183
[25] Rao C.R (1965) The use and interpretation of principal component analysis in applied research. Sankhya A 26, 329-358 · Zbl 0137.37207
[26] Robert P, Escoufier Y (1976) A unifying tool for linear multivariate statistical methods: the RV — coefficient. Appl.Statist. 25, 257-265
[27] Sabatier R, Vivien M (2004) A new linear method for analyzing four — way multibloks tables: STATIS — 4 submitted to Computational Statistics & Data analysis
[28] Sabatier R, Jan Y, Escoufier Y (1984) Approximations d’applications linéaires et analyse en composantes principales In: E. Diday et al.(eds) Data Analysis and informatics III. Elsevier Science Publishers B.V. (North-Holland) · Zbl 0566.62045
[29] Schlich P (1996) Defining and validating assessor compromises about product distances and attributes correlations. In: Naes T. and Risvik E (eds) Multivariate analysis of data in sensory science. Elesevier Science B.V.
[30] Schlich P, Guichard E (1989) Selection and classification of volatile compounds of abricot using the RV coefficient. Journal of Agricultural and Food Chemistry, 37, 142-150
[31] Vivien M, Sabatier R (2004) A generalization of STATIS — ACT strategy: Do ACT for multiblocks tables. Computational Statistics & data Analysis 46, 155- · Zbl 1429.62229
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