Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

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References 431in Descriptive Multivariate Analysis, ed. W.J. Krzanowski, 190–226.Oxford: Clarendon Press.Gabriel K.R. (1995b). MANOVA biplots for two-way contingency tables.In Recent Advances in Descriptive Multivariate Analysis, ed. W.J.Krzanowski, 227–268. Oxford: Clarendon Press.Gabriel, K.R. (2002). Goodness of fit of biplots and correspondenceanalysis. To appear in Biometrika.Gabriel, K.R. and Odoroff C.L. (1983). Resistant lower rank approximationof matrices. Technical report 83/02, Department of Statistics, Universityof Rochester, New York.Gabriel, K.R. and Odoroff, C.L. (1990). Biplots in biomedical research.Statist. Med., 9, 469–485.Gabriel, K.R. and Zamir, S. (1979). Lower rank approximation of matricesby least squares with any choice of weights. Technometrics, 21, 489–498.Garnham, N. (1979). Some aspects of the use of principal components inmultiple regression. Unpublished M.Sc. dissertation. University of Kentat Canterbury.Garthwaite, P.H. (1994). An interpretation of partial least squares. J.Amer. Statist. Assoc., 89, 122–127.Gauch, H.G. (1982). Multivariate Analysis in Community Ecology. Cambridge:Cambridge University Press.Geladi, P. (1988). Notes on the history and nature of partial least squares(PLS) modelling. J. Chemometrics, 2, 231–246.Gifi, A. (1990). Nonlinear Multivariate Analysis. Chichester: Wiley.Girshick, M.A. (1936). Principal components. J. Amer. Statist. Assoc., 31,519–528.Girshick, M.A. (1939). On the sampling theory of roots of determinantalequations. Ann. Math. Statist., 10, 203–224.Gittins, R. (1969). The application of ordination techniques. In EcologicalAspects of the Mineral Nutrition of Plants, ed. I. H. Rorison, 37–66.Oxford: Blackwell Scientific Publications.Gittins, R. (1985). Canonical Analysis. A Review with Applications inEcology. Berlin: Springer.Gleason, T.C. and Staelin, R. (1975). A proposal for handling missing data.Psychometrika, 40, 229–252.Gnanadesikan, R. (1977). Methods for Statistical Data Analysis of MultivariateObservations. New York: Wiley.Gnanadesikan, R. and Kettenring, J.R. (1972). Robust estimates, residuals,and outlier detection with multiresponse data. Biometrics, 28, 81–124.Goldstein, H. (1995). Multilevel Statistical Models, 2nd edition. London:Arnold.Goldstein, M. and Dillon, W.R. (1978). Discrete Discriminant Analysis.New York: Wiley.
432 ReferencesGolyandina, N.E., Nekrutin, V.V. and Zhigljavsky, A.A. (2001). Analysisof Time Series Structure. SSA and Related Techniques. Boca Raton:Chapman and Hall.Gonzalez, P.L., Evry, R., Cléroux, R. and Rioux, B. (1990). Selecting thebest subset of variables in principal component analysis. In COMP-STAT 90, eds. K. Momirovic and V. Mildner, 115–120. Heidelberg:Physica-Verlag.Good, I.J. (1969). Some applications of the singular value decompositionof a matrix. Technometrics, 11, 823–831.Gordon, A.D. (1999). Classification, 2nd edition. Boca Raton: Chapmanand Hall/CRC.Gower, J.C. (1966). Some distance properties of latent root and vectormethods used in multivariate analysis. Biometrika, 53, 325–338.Gower, J.C. (1967). Multivariate analysis and multidimensional geometry.Statistician, 17, 13–28.Gower, J.C. and Hand, D.J. (1996). Biplots. London: Chapman and Hall.Gower, J.C. and Krzanowski, W.J. (1999). Analysis of distance for structuredmultivariate data and extensions to multivariate analysis ofvariance. Appl. Statist., 48, 505–519.Grambsch, P.M., Randall, B.L., Bostick, R.M., Potter, J.D. and Louis,T.A. (1995). Modeling the labeling index distribution: An application offunctional data analysis. J. Amer. Statist. Assoc., 90, 813–821.Green, B.F. (1977). Parameter sensitivity in multivariate methods. J.Multiv. Behav. Res., 12, 263–287.Greenacre, M.J. (1984). Theory and Applications of CorrespondenceAnalysis. London: Academic Press.Greenacre, M.J. (1993). Correspondence Analysis in Practice. London:Academic Press.Greenacre, M. and Hastie, T. (1987). The geometric interpretation ofcorrespondence analysis. J. Amer. Statist. Assoc., 82, 437–447.Grimshaw, S.D., Shellman, S.D. and Hurwitz, A.M. (1998). Real-timeprocess monitoring for changing inputs. Technometrics, 40, 283–296.Grossman, G.D., Nickerson, D.M. and Freeman, M.C. (1991). Principalcomponent analyses of assemblage structure data: Utility of tests basedon eigenvalues. Ecology, 72, 341–347.Guiot, J. (1981). Analyse Mathématique de Données Geophysique. Applicationsà la Dendroclimatologie. Unpublished Ph.D. dissertation, UniversitéCatholique de Louvain.Gunst, R.F. (1983). Regression analysis with multicollinear predictor variables:Definition, detection and effects. Commun. Statist.—Theor. Meth.,12, 2217–2260.Gunst, R.F. and Mason, R.L. (1977a). Biased estimation in regression:An evaluation using mean squared error. J. Amer. Statist. Assoc., 72,616–628.
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Principal ComponentAnalysis,Second
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viPreface to the Second Editionerty
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viiiPreface to the Second EditionA
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xPreface to the First Editionand in
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xiiPreface to the First EditionIn m
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xviAcknowledgmentsthese institution
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xviiiContents3.4.1 Example ........
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xxContents10 Outlier Detection, Inf
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xxivList of Figures5.2 Artistic qua
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xxviiiList of Tables6.1 First six e
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2 1. IntroductionFigure 1.1. Plot o
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4 1. IntroductionFigure 1.3. Studen
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1.2. A Brief History of Principal C
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1.2. A Brief History of Principal C
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2.1. Optimal Algebraic Properties o
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2.2. Geometric Properties of Popula
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2.3. Principal Components Using a C
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2.4. Principal Components with Equa
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3Mathematical and StatisticalProper
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where3.1. Optimal Algebraic Propert
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3.2. Geometric Properties of Sample
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3.3. Covariance and Correlation Mat
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3.3. Covariance and Correlation Mat
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3.4. Principal Components with Equa
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show that X = ULA ′ .⎡ULA ′ =
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3.6. Probability Distributions for
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3.7. Inference Based on Sample Prin
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3.7.2 Interval Estimation3.7. Infer
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3.8. Patterned Covariance and Corre
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3.9. Models for Principal Component
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3.9. Models for Principal Component
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4Principal Components as a SmallNum
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4.1. Anatomical Measurements 65Tabl
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4.1. Anatomical Measurements 67spac
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4.2. The Elderly at Home 69Table 4.
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4.3. Spatial and Temporal Variation
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4.3. Spatial and Temporal Variation
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4.4. Properties of Chemical Compoun
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4.5. Stock Market Prices 77Table 4.
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5. Graphical Representation of Data
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Anatomical Measurements5.1. Plottin
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5.1. Plotting Two or Three Principa
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5.2. Principal Coordinate Analysis
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5.3. Biplots 91columns, L is an (r
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5.3. Biplots 93ButandSubstituting i
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5.3. Biplots 95The vector gi ∗ co
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5.3. Biplots 97Figure 5.3. Biplot u
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5.3. Biplots 99Table 5.2. First two
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5.3. Biplots 101Figure 5.5. Biplot
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5.4. Correspondence Analysis 103of
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5.4. Correspondence Analysis 105Fig
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5.6. Displaying Intrinsically High-
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5.6. Displaying Intrinsically High-
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6Choosing a Subset of PrincipalComp
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6.1. How Many Principal Components?
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6.2. Choosing m, the Number of Comp
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6.2. Choosing m, the Number of Comp
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6.3. Selecting a Subset of Variable
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6.4. Examples Illustrating Variable
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7.1. Models for Factor Analysis 151
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7.2. Estimation of the Factor Model
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7.3. Comparisons Between Factor and
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7.4. An Example of Factor Analysis
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7.4. An Example of Factor Analysis
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7.5. Concluding Remarks 165To illus
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8Principal Components in Regression
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8.1. Principal Component Regression
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8.1. Principal Component Regression
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8.2. Selecting Components in Princi
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8.2. Selecting Components in Princi
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8.3. Connections Between PC Regress
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8.4. Variations on Principal Compon
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8.5. Variable Selection in Regressi
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8.5. Variable Selection in Regressi
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8.6. Functional and Structural Rela
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8.7. Examples of Principal Componen
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Table 8.3. Principal component regr
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9Principal Components Used withOthe
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9.1. Discriminant Analysis 201on th
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9.1. Discriminant Analysis 203Figur
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9.1. Discriminant Analysis 205Corbi
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9.1. Discriminant Analysis 207that
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9.1. Discriminant Analysis 209betwe
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9.2. Cluster Analysis 211dimensiona
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9.2. Cluster Analysis 213Before loo
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9.2. Cluster Analysis 215Figure 9.3
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9.2. Cluster Analysis 217demographi
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9.2. Cluster Analysis 219county clu
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9.2. Cluster Analysis 221choosing a
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9.3. Canonical Correlation Analysis
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10.1. Detection of Outliers Using P
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10.2. Influential Observations in a
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10.3. Sensitivity and Stability 259
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10.3. Sensitivity and Stability 261
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10.4. Robust Estimation of Principa
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11Rotation and Interpretation ofPri
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11.1. Rotation of Principal Compone
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oot of the corresponding eigenvalue
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11.2. Alternatives to Rotation 279w
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11.2. Alternatives to Rotation 281F
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11.2. Alternatives to Rotation 283F
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11.2. Alternatives to Rotation 285T
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11.2. Alternatives to Rotation 287T
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11.2. Alternatives to Rotation 289A
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11.2. Alternatives to Rotation 291
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11.3. Simplified Approximations to
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11.3. Simplified Approximations to
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11.4. Physical Interpretation of Pr
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12Principal Component Analysis forT
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12.1. Introduction 301series is alm
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12.2. PCA and Atmospheric Time Seri
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and a typical row of the matrix is1
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12.3. Functional PCA 317A key refer
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12.3. Functional PCA 319The sample
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12.3. Functional PCA 321speed (mete
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12.3. Functional PCA 323of the data
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12.3. Functional PCA 325subject to
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12.3. Functional PCA 327series than
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12.4. PCA and Non-Independent Data
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13.1. Principal Component Analysis
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13.2. Analysis of Size and Shape 34
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13.2. Analysis of Size and Shape 34
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13.5. Common Principal Components 3
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13.7. PCA in Statistical Process Co
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13.8. Some Other Types of Data 369A
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13.8. Some Other Types of Data 371d
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14Generalizations and Adaptations o
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14.1. Non-Linear Extensions of Prin
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14.1. Additive Principal Components
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14.1. Additive Principal Components
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Page 432 and 433: 14.6. Miscellanea 401• Linear App
Page 434 and 435: 14.6. Miscellanea 40314.6.3 Regress
Page 436 and 437: 14.7. Concluding Remarks 405space o
Page 438 and 439: Appendix AComputation of Principal
Page 440 and 441: A.1. Numerical Calculation of Princ
Page 446 and 447: ReferencesAguilera, A.M., Gutiérre
Page 448 and 449: References 417Apley, D.W. and Shi,
Page 450 and 451: References 419Benasseni, J. (1986b)
Page 452 and 453: References 421Boik, R.J. (1986). Te
Page 454 and 455: References 423Castro, P.E., Lawton,
Page 456 and 457: References 425Cook, R.D. (1986). As
Page 458 and 459: References 427Dempster, A.P., Laird
Page 460 and 461: References 429Feeney, G.J. and Hest
Page 464 and 465: References 433Gunst, R.F. and Mason
Page 466 and 467: References 435Hocking, R.R., Speed,
Page 468 and 469: References 437Jeffers, J.N.R. (1978
Page 470 and 471: References 439Kazi-Aoual, F., Sabat
Page 472 and 473: References 441Krzanowski, W.J. (200
Page 474 and 475: References 443Mann, M.E. and Park,
Page 476 and 477: References 445Monahan, A.H., Tangan
Page 478 and 479: References 447Pack, P., Jolliffe, I
Page 480 and 481: References 449Richman M.B. (1993).
Page 482 and 483: References 451Soofi, E.S. (1988). P
Page 484 and 485: References 453Tenenbaum, J.B., de S
Page 486 and 487: References 455Vong, R., Geladi, P.,
Page 488 and 489: References 457regularities in multi
Page 490 and 491: Index 459116, 127-130, 133, 270, 27
Page 492 and 493: Index 461computationin (PC) regress
Page 494 and 495: Index 463discriminant principal com
Page 496 and 497: Index 465of correlations between va
Page 498 and 499: Index 467see also hypothesis testin
Page 500 and 501: Index 469PC algorithms with noise 4
Page 502 and 503: Index 471in functional and structur
Page 504 and 505: Index 473variance ellipsoids,S-esti
Page 506 and 507: Index 475spatial correlation/covari
Page 508 and 509: Index 477for covariance matrices 26
Page 510 and 511: Author Index 479Belsley, D.A. 169Be
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Author Index 481Fowlkes, E.B. 377Fr
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Author Index 483Krzanowski, W.J. 46
Page 516 and 517:
Author Index 485Rencher, A.C. 64, 1
Page 518:
Author Index 487Yaguchi, H. 371Yana
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