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

470 Indexpattern recognition 200patterned correlation/covariancematrices 27, 30, 56–58all correlations equal 27, 55, 56all correlations positive 57, 58,67, 84, 99, 145, 148, 162,174, 245all correlations (near) zero 54,55, 206, 348groups of correlated variables56–58, 114, 138, 167, 196,213widely differing variances 22, 40,56, 115, 134, 135see also structure of PCs,Töplitz matricesPC coefficientsalternative terminology 6, 72arbitrariness of sign 67hypothesis testing 53interval estimation 52maps of coefficients 72, 73, 80,275, 284–283point estimation 50, 66use in variable selection 138,138, 141see also comparisons betweenPCs, computation of PCs,discrete PC coefficients, firstfew PCs, influence functionsfor PC coefficients, lastfew PCs, normalizationconstraints, probabilitydistributions, roundedPC coefficients, samplingvariation, simplified PCcoefficients, stability ofPCs, structure of PCsPC loadings see PC coefficientsPC regression 32, 123, 167–199,202, 245, 337, 352computation 46, 173, 408, 412interpretation 170, 173locally weighted 185PC scores 30, 31, 36, 39, 45, 72,169, 238, 265, 342, 362, 413PC series, see point estimationPC varianceshypothesis testing 53–55, 114,117–120, 128, 129, 136interval estimation 51, 52lower bounds 57point estimation 50tests for equality 53–55, 118,119, 128, 134see also Bartlett’s test,computation of PCs,first few PCs, influencefunctions for PC variances,last few PCs, probabilitydistributions, rules forselecting PCs, samplingvariationPCA based on Euclidean similarity391PCA of residuals/errors 240, 304,352, 353, 365, 391, 394see also interactionspenalty function 278roughness penalty 325, 326, 377periodically extended EOFs314-316permutational PCs 339, 340perturbed data 259–262physical interpretionin ICA 396of PCs 132, 270, 296–298, 320modes of the atmosphere 132,296, 297, 391Pisarenko’s method 303pitprops 190–194, 286, 287, 289point estimationfor factor loadings 151–157for factor scores 153, 160for PC coefficients 50, 66for PC series 329for PC variances 50in econometrics 393, 394