Page 505 - Jolliffe I. Principal Component Analysis

Index
470
pattern recognition 200
169, 238, 265, 342, 362, 413
patterned correlation/covariance
matrices 27, 30, 56–58 PC scores 30, 31, 36, 39, 45, 72,
PC series, see point estimation
all correlations equal 27, 55, 56 PC variances
all correlations positive 57, 58, hypothesis testing 53–55, 114,
67, 84, 99, 145, 148, 162, 117–120, 128, 129, 136
174, 245 interval estimation 51, 52
all correlations (near) zero 54, lower bounds 57
55, 206, 348 point estimation 50
groups of correlated variables tests for equality 53–55, 118,
56–58, 114, 138, 167, 196, 119, 128, 134
213 see also Bartlett’s test,
widely differing variances 22, 40, computation of PCs,
56, 115, 134, 135 first few PCs, influence
see also structure of PCs, functions for PC variances,
T¨oplitz matrices last few PCs, probability
PC coefficients distributions, rules for
alternative terminology 6, 72 selecting PCs, sampling
arbitrariness of sign 67 variation
hypothesis testing 53 PCA based on Euclidean similarity
interval estimation 52 391
maps of coefficients 72, 73, 80, PCA of residuals/errors 240, 304,
275, 284–283 352, 353, 365, 391, 394
point estimation 50, 66 see also interactions
penalty function 278
use in variable selection 138,
138, 141 roughness penalty 325, 326, 377
see also comparisons between periodically extended EOFs
PCs, computation of PCs, 314-316
discrete PC coefficients, first permutational PCs 339, 340
few PCs, influence functions perturbed data 259–262
for PC coefficients, last physical interpretion
few PCs, normalization in ICA 396
constraints, probability of PCs 132, 270, 296–298, 320
distributions, rounded modes of the atmosphere 132,
PC coefficients, sampling 296, 297, 391
variation, simplified PC Pisarenko’s method 303
coefficients, stability of pitprops 190–194, 286, 287, 289
PCs, structure of PCs point estimation
PC loadings see PC coefficients for factor loadings 151–157
PC regression 32, 123, 167–199, for factor scores 153, 160
202, 245, 337, 352 for PC coefficients 50, 66
computation 46, 173, 408, 412 for PC series 329
interpretation 170, 173 for PC variances 50
locally weighted 185 in econometrics 393, 394