Rencher A.C., Barnett V., Bradley R.A. (Ed) — Multivariate Statistical Inference and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Rencher A.C., Barnett V., Bradley R.A. (Ed) — Multivariate Statistical Inference and Applications

Rencher A.C., Barnett V., Bradley R.A. (Ed) — Multivariate Statistical Inference and Applications

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Название: Multivariate Statistical Inference and Applications

Авторы: Rencher A.C., Barnett V., Bradley R.A. (Ed)

Аннотация:

The most accessible introduction to the theory and practice of multivariate analysis

Multivariate Statistical Inference and Applications is a user-friendly introduction to basic multivariate analysis theory and practice for statistics majors as well as nonmajors with little or no background in theoretical statistics. Among the many special features of this extremely accessible first text on multivariate analysis are:
* Clear, step-by-step explanations of all key concepts and procedures along with original, easy-to-follow proofs
* Numerous problems, examples, and tables of distributions
* Many real-world data sets drawn from a wide range of disciplines
* Reviews of univariate procedures that give rise to multivariate techniques
* An extensive survey of the world literature on multivariate analysis
* An in-depth review of matrix theory
* A disk including all the data sets and SAS command files for all examples and numerical problems found in the book

These same features also make Multivariate Statistical Inference and Applications an excellent professional resource for scientists and clinicians who need to acquaint themselves with multivariate techniques. It can be used as a stand-alone introduction or in concert with its more methods-oriented sibling volume, the critically acclaimed Methods of Multivariate Analysis.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 592

Добавлена в каталог: 12.05.2008

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Предметный указатель

Expected value of sample variance       3
Expected value of sum or product of random variables      5
Expected value of univariate random variable [E(y)]      2
Experimentwise error rates      2
F-test(s) and       67
F-test(s), partial F-test for discriminant functions      211
F-test(s), partial F-test in MANOVA      110
F-test(s), tables of power of the F-test      423—426
Factor analysis      377—398
Factor analysis and grouped data      393—394
Factor analysis and regression      394—395
Factor analysis of correlation matrix      379—380. 383 385—386. 392
Factor analysis of covariance matrix      377—388. 391—395
Factor analysis, and principal components      361 377
Factor analysis, applicability of the model      392—393
Factor analysis, assumptions      378—379
Factor analysis, communality      379 381
Factor analysis, eigenvalues      381—383
Factor analysis, eigenvectors      381
Factor analysis, factor scores      391—392
Factor analysis, factors      377—379
Factor analysis, factors, interpretation of      378 381 390—391
Factor analysis, fit of the model      392—393
Factor analysis, loadings      378 381—385
Factor analysis, loadings, estimation of      381—385
Factor analysis, loadings, estimation of, comparison of methods      385—386
Factor analysis, loadings, estimation of, iterated principal factor method      384
Factor analysis, loadings, estimation of, maximum likelihood method      384—385
Factor analysis, loadings, estimation of, principal axis method      383—384
Factor analysis, loadings, estimation of, principal component method      381—383
Factor analysis, loadings, estimation of, principal factor method      383—384
Factor analysis, model      378—379
Factor analysis, model, scale invariance of      379—380
Factor analysis, nonlinear models      394
Factor analysis, number of factors to retain      381 386—387
Factor analysis, robustness to nonnormality      394
Factor analysis, rotation of loadings in the model      380
Factor analysis, rotation of sample loadings and factors      387—390
Factor analysis, rotation of sample loadings and factors, interpretation of factors      390—391
Factor analysis, rotation of sample loadings and factors, oblique rotation      389—390
Factor analysis, rotation of sample loadings and factors, oblique rotation, pattern matrix      390
Factor analysis, rotation of sample loadings and factors, oblique rotation, structure matrix      390
Factor analysis, rotation of sample loadings and factors, orthogonal rotation      388—389
Factor analysis, rotation of sample loadings and factors, orthogonal rotation, equamax      389
Factor analysis, rotation of sample loadings and factors, orthogonal rotation, quartimax      389
Factor analysis, rotation of sample loadings and factors, orthogonal rotation, varimax      388
Factor analysis, specific variance      379
Factor analysis, tests of significance      386—387
Factor analysis, three-mode factor analysis      394
Factor analysis, total variance      382
Fisher’s LSD test      134
Fracture data      171
Function of a random variable, distribution of      38—40
Gauss — Markov theorem, multivariate      284—285
Gauss — Markov theorem, univariate      268
Generalized linear models      266
Generalized quadratic form      54—55
Generalized variance      8—9 40
Glucose data      35
H matrix      122 203
Height-weight data      4
Hierarchical linear models      306
Hotelling’s       see “ $T^2$

$T^2$

-tests”
Hypothesis tests      see “Tests of hypotheses”
Idempotent matrix      414
Identity matrix      400
Imputation      see “Missing data”
Independence and zero covariance      5 46—47
Independence, two random variables      5
Independence, two random vectors      46
Influence and canonical correlation      333
Influence and canonical variates      333
Influence and classification analysis      262
Influence and discriminant analysis (descriptive)      206
Influence and multivariate regression      301—303
Influence and principal components      372—373
Intercorrelation, index of      20—22
Intercorrelation, index of, condition number      20
Intercorrelation, index of, variance inflation factor      21
Inverse matrix      407
j vector and J matrix      400
Jackknife      327
Jacobian      39
Largest root test      see “Roy’s test”
Latent root regression      363 370
Latent roots      see “Eigenvalues”
Lawley — Hotelling test      130—131 292 295—296
Lawley — Hotelling test, F-approximations      130—131
Lawley — Hotelling test, table of critical values      441—445
Least squares estimators      267—268 281—282
Length of a vector      402
Library data      397
Likelihood function      49
Likelihood ratio      62—65
Likelihood ratio test for discriminant functions      209
Likelihood ratio test in canonical correlation      321—326
Likelihood ratio test in multivariate regression      289—299
Likelihood ratio test in principal components      349—351 357—359
Likelihood ratio test in random-x regression      279
Likelihood ratio test, comparing covariance matrices      138
Likelihood ratio test, generalized likelihood ratio      262
Likelihood ratio test, one-sample -test      71—72
Likelihood ratio test, one-sample t-test      62—65
Likelihood ratio test, one-way MANOVA      122—126
Likelihood ratio test, random effects MANOVA      111
Likelihood ratio test, two-sample -test      91—92
Likelihood ratio test, two-sample t-test      85—86
Linear classification functions      231—232 236
Linear classification rule      231—232 236
Linear function(s) of random variables      14—20
Linear function(s) of random variables, confidence intervals for      74 92—94
Linear function(s) of random variables, correlation of two linear combinations      15 20
Linear function(s) of random variables, covariance matrix for several linear combinations      15—16 20
Linear function(s) of random variables, covariance matrix for two sets of linear combinations      16 20
Linear function(s) of random variables, covariance of two linear combinations      15 19
Linear function(s) of random variables, linear combinations of subvectors      16—17 20
Linear function(s) of random variables, mean of a single linear combination      14 19
Linear function(s) of random variables, variance of a single linear combination      15 19
Linear hypotheses in ANOVA and MANOVA      163—171
Linear hypotheses in multivariate regression      295—297
Linear hypotheses in univariate regression      272—273
Linear hypotheses, one sample      72—74 79—80 83—85
Linear hypotheses, one sample, for : $\mu_1 = \mu_2 = . . . = \mu_p$       83—85
Linear hypotheses, two samples      94—95
Log linear models      2
Logistic classification      254—259
Logistic classification, comparison with linear classification      256—257
Logistic classification, quadratic logistic classification      258
Logistic classification, several groups      258
Logistic regression      254—255
Longley data      368
LSD test      134
Mahalanobis distance      22—23
Manova      121 (see also “Multivariate analysis of variance”)
Matrix (matrices), addition of      401
Matrix (matrices), algebra of      399—416
Matrix (matrices), bilinear form      404
Matrix (matrices), centering matrix      9—10
Matrix (matrices), characteristic equation      411
Matrix (matrices), Cholesky decomposition      42 408
Matrix (matrices), correlation matrix      11—12 (see also “Correlation matrix”)
Matrix (matrices), covariance matrix      8—9 (see also “Co variance matrix”)
Matrix (matrices), covariance matrix, positive definite      9—10
Matrix (matrices), data matrix      7
Matrix (matrices), definition      399
Matrix (matrices), determinant      409
Matrix (matrices), diagonal matrix      11 400
Matrix (matrices), diagonal of a matrix      400
Matrix (matrices), differentiation      50—51 414—416
Matrix (matrices), eigenvalues      411—414 (see also “Eigenvalues”)

Matrix (matrices), eigenvalues and determinant      411
Matrix (matrices), eigenvalues and trace      411
Matrix (matrices), eigenvalues of inverse      411
Matrix (matrices), eigenvalues of positive definite matrix      412
Matrix (matrices), eigenvalues of product      411
Matrix (matrices), eigenvalues of symmetric matrix      412
Matrix (matrices), eigenvalues, characteristic equation      411
Matrix (matrices), eigenvectors      411—414 (see also “Eigenvectors”)
Matrix (matrices), factoring of      402
Matrix (matrices), idempotent matrix      414
Matrix (matrices), identity      400
Matrix (matrices), inverse      407
Matrix (matrices), inverse of partitioned matrix      407
Matrix (matrices), inverse of product      407
Matrix (matrices), J matrix      400
Matrix (matrices), j vector      400
Matrix (matrices), multiplication of      401
Matrix (matrices), nonsingular matrix      407
Matrix (matrices), O (zero matrix)      401
Matrix (matrices), operations with      401—406
Matrix (matrices), operations with, distributive law      401
Matrix (matrices), operations with, factoring      402
Matrix (matrices), operations with, product      401—406
Matrix (matrices), operations with, product of matrix and vector      405
Matrix (matrices), operations with, product of matrix and vector as linear combination      405
Matrix (matrices), operations with, product of vectors      401—402
Matrix (matrices), operations with, product, noncommutativity of      401
Matrix (matrices), operations with, product, with diagonal matrix      404
Matrix (matrices), operations with, sum      401—402
Matrix (matrices), operations with, sum, commutativity of      401
Matrix (matrices), orthogonal matrices      410
Matrix (matrices), partitioned matrices      404—406
Matrix, Perron — Frobenius theorem      414
Matrix, positive definite matrix      408
Matrix, positive semidefinite matrix      408
Matrix, products      401 404
Matrix, quadratic form      48—49 404
Matrix, quadratic form, generalized quadratic form      54—55
Matrix, random matrix, expected value of      10
Matrix, rank      406
Matrix, rank, full rank      406
Matrix, singular matrix      407 408
Matrix, size of a matrix      399
Matrix, spectral decomposition      412
Matrix, square root matrix      413
Matrix, trace      410
Matrix, triangular matrix      400
Matrix, vectors      see “Vector(s)”
Matrix, zero matrix (O) and zero vector (0)      401
Maximum likelihood estimators      49—52
Maximum likelihood estimators in regression      286—289
Maximum likelihood estimators of covariance matrix      49—51
Maximum likelihood estimators of mean vector      49—51
Maximum likelihood estimators, invariance property of      51—52
Maximum likelihood estimators, likelihood function      49
Maximum likelihood estimators, multivariate normal      49
Mean      see also “Expected value”
Mean deviation      28
Mean population      2
Mean sample      2
Mean vector, partitioned      12—13
Mean vector, population      8
Mean vector, sample      7
Misclassification rates      see “Error rate(s)”
Missing data      23—27 299—300
Missing data and classification analysis      262—263
Missing data and hypothesis tests      299—300
Missing data, estimation of missing values (imputation)      24—27
Missing data, listwise deletion      23
Missing data, missing at random      23
Missing data, missing completely at random      23
Missing data, pairwise deletion      24
Models, generalized linear models      2
Models, log linear models      2
Moment generating function      43—45
Moments      42—43
Multicolinearity      40 327 364 368
Multidimensional scaling      373
Multiple correlation      275 (see also “R^2”)
Multiple regression      see “Regression multiple”
Multivariate analysis      1
Multivariate analysis of covariance      see “Analysis of covariance multivariate”
Multivariate analysis of variance (Manova)      121—200
Multivariate analysis of variance (MANOVA) and canonical correlation      312 333
Multivariate analysis of variance (MANOVA) and eigenvalues      131
Multivariate analysis of variance (MANOVA), additional information, test for      174—178
Multivariate analysis of variance (MANOVA), approximate tests, based on M-estimators      194
Multivariate analysis of variance (MANOVA), approximate tests, based on ranks      194
Multivariate analysis of variance (MANOVA), contrasts      145—148 150—151
Multivariate analysis of variance (MANOVA), contrasts, orthogonal      146
Multivariate analysis of variance (MANOVA), contrasts, simultaneous      146—148
Multivariate analysis of variance (MANOVA), discriminant functions      157
Multivariate analysis of variance (MANOVA), discriminant, functions      128 151 “Discriminant
Multivariate analysis of variance (MANOVA), Fisher’s LSD test      134
Multivariate analysis of variance (MANOVA), H and E matrices      122 124
Multivariate analysis of variance (MANOVA), higher order models      151
Multivariate analysis of variance (MANOVA), individual variables, tests on      134
Multivariate analysis of variance (MANOVA), Lawley — Hotelling test      130—131
Multivariate analysis of variance (MANOVA), Lawley — Hotelling test, F-approximations      130—131
Multivariate analysis of variance (MANOVA), Lawley — Hotelling test, table of critical values      441—445
Multivariate analysis of variance (MANOVA), likelihood ratio test      see “Wilks’ $\Lambda$ ”
Multivariate analysis of variance (MANOVA), mixed models      151
Multivariate analysis of variance (MANOVA), one-way classification      121—134
Multivariate analysis of variance (MANOVA), one-way classification, contrasts      145—148
Multivariate analysis of variance (MANOVA), one-way classification, unbalanced data      155—160
Multivariate analysis of variance (MANOVA), one-way model      155—160
Multivariate analysis of variance (MANOVA), Pillai’s test      130—131
Multivariate analysis of variance (MANOVA), Pillai’s test, F-approximations      130
Multivariate analysis of variance (MANOVA), Pillai’s test, table of critical values      435—437
Multivariate analysis of variance (MANOVA), power of the tests      137—138 140—142
Multivariate analysis of variance (MANOVA), power of the tests, tables of power of the F-test      423—426
Multivariate analysis of variance (MANOVA), robustness of test statistics      137—138
Multivariate analysis of variance (MANOVA), Roy’s test (union-intersection)      127—129
Multivariate analysis of variance (MANOVA), Roy’s test (union-intersection), table of critical values      435—437
Multivariate analysis of variance (MANOVA), selection of variables, stepwise      177
Multivariate analysis of variance (MANOVA), step-down test      177
Multivariate analysis of variance (MANOVA), stepwise discriminant analysis      177—178
Multivariate analysis of variance (MANOVA), test on individual variables      134
Multivariate analysis of variance (MANOVA), test statistics and eigenvalues      131
Multivariate analysis of variance (MANOVA), test statistics, comparison of      132 135—138
Multivariate analysis of variance (MANOVA), test statistics, power of      137—138 140—142
Multivariate analysis of variance (MANOVA), test statistics, robustness of      137—138
Multivariate analysis of variance (MANOVA), tests on a subvector      174—178
Multivariate analysis of variance (MANOVA), tests on individual variables      157
Multivariate analysis of variance (MANOVA), tests on individual variables, experimentwise error rate      134
Multivariate analysis of variance (MANOVA), tests on individual variables, protected tests      134
Multivariate analysis of variance (MANOVA), two-way classification      148—151
Multivariate analysis of variance (MANOVA), two-way classification, contrasts      150—151
Multivariate analysis of variance (MANOVA), two-way classification, discriminant functions      151
Multivariate analysis of variance (MANOVA), two-way classification, interaction      148—149
Multivariate analysis of variance (MANOVA), two-way classification, main effects      148—149
Multivariate analysis of variance (MANOVA), two-way classification, model      148
Multivariate analysis of variance (MANOVA), two-way classification, test statistics      149
Multivariate analysis of variance (MANOVA), two-way model      168—174
Multivariate analysis of variance (MANOVA), two-way model, constrained model      169—171
Multivariate analysis of variance (MANOVA), unbalanced data      152 155—160 168—174
Multivariate analysis of variance (MANOVA), unbalanced data, Bonferroni confidence intervals      157
Multivariate analysis of variance (MANOVA), unbalanced data, contrasts      156—160
Multivariate analysis of variance (MANOVA), unbalanced data, simultaneous confidence intervals      156—157
Multivariate analysis of variance (MANOVA), union-intersection test      see “Roy’s test”
Multivariate analysis of variance (MANOVA), Wilks’ A (likelihood ratio)      122—126
Multivariate analysis of variance (MANOVA), Wilks’ A (likelihood ratio), Chi-square approximation      126
Multivariate analysis of variance (MANOVA), Wilks’ A (likelihood ratio), effect of each variable      132—134
Multivariate analysis of variance (MANOVA), Wilks’ A (likelihood ratio), F-approximation      125—126
Multivariate analysis of variance (MANOVA), Wilks’ A (likelihood ratio), properties of      124—126
Multivariate analysis of variance (MANOVA), Wilks’ A (likelihood ratio), table of critical values      427—434
Multivariate analysis of variance (MANOVA), Wilks’ A (likelihood ratio), transformations to exact F      125—126
Multivariate central limit theorem      53
Multivariate data      1—2 7
Multivariate descriptive procedures      1

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