Page 502 - Jolliffe I. Principal Component Analysis

see also hypothesis testing for
equality of PC variances,
near-constant relationships, LR algorithm 411 Index 467
M-estimators 264, 265, 267
residuals after fitting first Mahalanobis distances 33, 93, 94,
few PCs, zero variance PCs 104, 203, 204, 209, 212, 237,
latent root regression 168, 178, 264, 265
180–182, 185–187, 190, 191, manufacturing processes 366–368
197, 239 matrix correlation 96, 140, 141
latent semantic indexing 90 matrix-valued data 370
latent variables 151, 165, 226, 230, maximum covariance analysis 225,
231 226, 229, 401
latent variable multivariate maximum likelihood estimation
regression 230, 231 220, 264
least squares estimation/estimators for common PCs 355
32, 34, 59, 157, 167–173, for covariance matrices 50, 336,
175–179, 181, 184, 185, 189, 363, 364
208, 229, 286, 288, 294, 304, for factor loadings 155–157
326, 382, 385 for functional and structural
see also partial least squares relationships 189
leverage points 240 for PC coefficients and variances
see also influential observations 8, 50, 365
likelihood ratio test 54, 55, 120, in PC models 60, 222, 267, 364,
353, 356, 360 386
linear approximation asymmetric measurement errors 151, 188, 189
PCA 401 medical applications
loadings see factor loadings, PC biomedical problems 395
coefficients clinical trials 40, 239
local authorities epidemiology 248, 336
British towns 71, 215 opthalmology 266
England and Wales 195–198, see also chemistry (blood
245–247 chemistry)
English counties 108–110, meteorology and climatology 8, 9,
215–219 90, 183, 213, 381
local PCA 381 atmospheric pressure 71–73, 401
log-eigenvalue (LEV) diagram cloudbase heights 211
115–118, 128, 134-136 cloud-seeding 339
log transform see transformed monsoon onset date 174
variables satellite meteorology 358
longitudinal data 328, 330, 331, wind data 369, 370
355 see also atmospheric science,
lower (or upper) triangular climate change/variation,
matrices 182, 411, 412 ENSO, NAO, temperatures
lower rank approximations to method of moments estimation
matrices 38, 46, 113, 120, for PC coefficients and
342, 365, 383, 385 variances 50