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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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Íàçâàíèå: Multivariate Statistical Inference and Applications

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

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1997

Êîëè÷åñòâî ñòðàíèö: 592

Äîáàâëåíà â êàòàëîã: 12.05.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Multivariate inferential procedures      1—2
Multivariate normal distribution      37—59
Multivariate normal distribution and quadratic form      48—49
Multivariate normal distribution, central limit theorem      51
Multivariate normal distribution, conditional distribution      47—48
Multivariate normal distribution, constant density ellipsoid      40—41
Multivariate normal distribution, contour plot      40—42
Multivariate normal distribution, estimation of $\mu$ and $\Sigma$      49—51
Multivariate normal distribution, estimation of $\mu$ and $\Sigma$, properties of estimators      52—56
Multivariate normal distribution, estimation of$ P_p$      51—52
Multivariate normal distribution, generating data from      42
Multivariate normal distribution, independence and zero covariance      46—47
Multivariate normal distribution, likelihood function      49
Multivariate normal distribution, linear functions of      45—46
Multivariate normal distribution, marginal distribution      46
Multivariate normal distribution, moment generating function of      44—47
Multivariate normal distribution, moments of      42—43
Multivariate normal distribution, properties of      43—49
Multivariate normal distribution, tests for multivariate normality      43
Multivariate normal distribution, transformations to achieve multivariate normality      56—57
Multivariate normal distribution, transformations to achieve multivariate normality and Wishart distribution      53—56
Multivariate normality, tests for      43
Multivariate regression      see “Regression multivariate”
Multivariate t-distribution      56
Nonparametric tests for several mean vectors      194
Nonparametric tests for two mean vectors      113
Normal distribution, multivariate normal      see “Multivariate normal distribution”
Normal distribution, univariate normal      37—38
Normal distribution, univariate normal, standard normal      37
Normality, tests for      43
O matrix      401
Orthogonal matrix      410
Orthogonal vectors      410
Outliers      43 301—303 373
Paired observation test      97—99
Partial F      177 211 214—215 217 219 248—249 252
Perron — Frobenius theorem      414
Physiological data      224
Pillai’s test      292 295 296
Pillai’s test, F-approximations      130
Pillai’s test, table of critical values      431—437
Pillai’s tests      130—131 292 295—296
Positive definite matrix      408
Power of a test      104—108
Power of a test, noncentrality parameter      104
Principal component regression      363—370
Principal components      337—376
Principal components and correspondence analysis      373
Principal components and eigenvalues      338 341
Principal components and eigenvectors      338
Principal components and factor analysis      361 377
Principal components and maximum variance      338
Principal components and minimum variance      339
Principal components and multidimensional scaling      373
Principal components and projections      340
Principal components and regression      363—370
Principal components and regression, biased regression      363
Principal components and regression, latent root regression      363 370
Principal components and regression, principal component regression      363—370
Principal components and regression, principal component regression, using correlation matrix      364 367—370
Principal components and regression, principal component regression, using covariance matrix      364—367
Principal components and regression, ridge regression      363
Principal components as rotation of axes      343—344
Principal components from covariance matrix (S)      338—344 348—355 357—363
Principal components of singular matrix      342
Principal components with grouped data      371—372
Principal components with grouped data, common principal components      371—372
Principal components with grouped data, comparing principal components      371—372
Principal components, common principal components      371—372
Principal components, correlations of      341—342
Principal components, definition      338
Principal components, discarding components      347—352
Principal components, discarding components, average eigenvalue      348
Principal components, discarding components, bootstrap      352
Principal components, discarding components, cross validation      352
Principal components, discarding components, jackknife      352
Principal components, discarding components, percent of variance      347
Principal components, discarding components, rank of $\Sigma$      352
Principal components, discarding components, scree graph      348—349
Principal components, discarding components, tests of significance      349—351
Principal components, empirical orthogonal functions      337
Principal components, from correlation matrix (R)      342 344—349 351 353—359 364 367—370
Principal components, from correlation matrix (R), properties of      344—345
Principal components, generalized principal components      340
Principal components, influence of each observation      372—373
Principal components, interpretation      353—363
Principal components, interpretation, correlations      361—363
Principal components, Karhunen — Loeve expansion      337
Principal components, large variance of a variable, effect of      342
Principal components, last few principal components      352—353
Principal components, leverage of each observation      372
Principal components, number of components to retain      see “Principal components discarding
Principal components, orthogonality of      339
Principal components, outliers      373
Principal components, percent of variance      341
Principal components, plotting of      340
Principal components, principal component regression      363—370
Principal components, principal curves      373
Principal components, principal points      373
Principal components, projection pursuit      340
Principal components, properties of      341—343
Principal components, proportion of variance      341
Principal components, robust principal components      373
Principal components, rotation      359—361
Principal components, scale invariance, lack of      342
Principal components, sensitivity analysis      355
Principal components, size and shape      355
Principal components, special patterns in S or R      353—359
Principal components, special patterns in S or R, equal correlations      354 358—359
Principal components, special patterns in S or R, equal variances and covariances      354 357—358
Principal components, special patterns in S or R, sensitivity analysis      355
Principal components, special patterns in S or R, size and shape      355
Principal components, tests of significance      349—351
Principal components, variance and eigenvalues      341
Principal components, variance of principal component      341
Principal components, variance, large variance, effect of      342
Principal components, variance, proportion of      341
Principal components, variance, total      341
Principal curves      373
Principal points      373
Probe word data      22
Projection pursuit      340
Projections      340
Quadratic classification rule      232—233
Quadratic form      48—49 404
Quadratic form, lack-of-fit tests      300
Quadratic form, leverage      301
Quadratic form, outliers      301—303
Quadratic form, residuals      300—301
Random x’s      303—305
Random x’s, confidence intervals      305
Random x’s, estimation of the $\beta$’s and $\Sigma$      304—305
Random x’s, estimation of the $\beta$’s and $\Sigma$, beta weights      305
Random x’s, estimation of the $\beta$’s and $\Sigma$, correlations      305
Random x’s, model      303—304
Random x’s, tests of hypotheses      305
Repeated measures      121 183 246 296
Robust estimation in classification analysis      235
Robust estimation in regression      307
Robust estimation of canonical variates      333
Robust estimation of correlation matrices      29—30
Robust estimation of covariance matrices      29—31
Robust estimation of discriminant functions      223—227
Robust estimation of mean vectors      28—31
Robust estimation of means      28
Robust estimation of principal components      373
Robust estimation, affine equivariance of (scale invariance)      30
Robust estimation, breakdown point      30
Robust estimation, contaminated normal      28
Robust estimation, mean deviation      28
Robust estimators      307
Rotation      see “Factor analysis”
Roy’s test      291—292 295 296
Roy’s test (union-intersection)      127—129 291—296
Roy’s test (union-intersection), table of critical values      435—437
Roy’s test, subset of the x’s      293—295
Roy’s test, union-intersection test      see “Roy’s test”
Roy’s test, Wilks’ $\Lambda$      290—291 294 296
Seemingly unrelated regression      306
Seemingly unrelated regressions      306
Selection of variables      111 177 217—221
Selection of variables in classification analysis      247—251
Selection of variables in higher order designs      218—219
Selection of variables in regression      307
Selection of variables, all possible subsets      218
Selection of variables, bias      219—221
Selection of variables, stepwise discriminant analysis      217—221
Selection of variables, using discriminant functions      217
Singular value decomposition      26—27 315—316
Size and shape      355
Soils data      103
Specific variance      379
Spectral decomposition      412
Squared multiple correlation      see “$R^2$”
SSE      269
SSR      271
Standardized vector      45
Stepdown test      110—111
Stepwise discriminant analysis      177—178 217—221
Subset selection      307
Subvector(s)      12—14
Subvector(s), conditional distribution      47
Subvector(s), covariance matrix of      13
Subvector(s), distribution of      46—48
Subvector(s), independence of      14
Subvector(s), mean of      13
Subvector(s), paired observation      116
Subvector(s), sum of      14
Subvector(s), tests on      108—112 174—178
Sufficient statistic      52—53
t-ests, definition of t-statistic      61
t-ests, likelihood ratio      62—65 86
t-ests, one sample      61—65
t-ests, properties of      62
t-ests, two samples      85—86
t-ests, two samples, comparing means when variances are unequal      99—100
Tests of hypotheses      289—300 305
Tests of hypotheses and missing data      299—300
Tests of hypotheses for additional information      108—110
Tests of hypotheses for an individual $\beta$      297
Tests of hypotheses for elliptically contoured distributions      112—113
Tests of hypotheses for linear combinations in ANOVA and MANOVA      163—171
Tests of hypotheses for linear combinations in multivariate regression      295—297
Tests of hypotheses for linear combinations in univariate regression      272—273
Tests of hypotheses for linear combinations one sample      72—72 79—80 83—85
Tests of hypotheses for linear combinations one sample, for $H_0$: \mu_1 = \mu_2 = . . . = \mu_p$      83—85
Tests of hypotheses for linear combinations, two samples      94—95
Tests of hypotheses for principal components      349—351
Tests of hypotheses in discriminant analysis      207—210
Tests of hypotheses in regression, multivariate      289—299
Tests of hypotheses in regression, univariate      271—274
Tests of hypotheses on a subvector      108—112 174—178
Tests of hypotheses, $T^2$-tests      see “$T^2$-tests”
Tests of hypotheses, $\Sigma$ known      60—61
Tests of hypotheses, $\Sigma$ unknown      65—74
Tests of hypotheses, $\Sigma$ unknown, several mean vectors      121—134
Tests of hypotheses, $\Sigma$ unknown, two mean vectors, $\Sigma_1= \Sigma_2$      85—92
Tests of hypotheses, $\Sigma$ unknown, two mean vectors, $\Sigma_1\neq \Sigma_2$,      100—104
Tests of hypotheses, accepting $H_0$      65
Tests of hypotheses, analysis of covariance, multivariate      see “Analysis of covariance multivariate”
Tests of hypotheses, analysis of covariance, univariate      see “Analysis of covariance univariate”
Tests of hypotheses, canonical correlation      320—326
Tests of hypotheses, covariance matrices, Box’s M-test      138—140
Tests of hypotheses, covariance matrices, equality of      138—140
Tests of hypotheses, covariance matrices, table of critical values      446—447
Tests of hypotheses, E matrix      285 286 290
Tests of hypotheses, equality of covariance matrices      138—140
Tests of hypotheses, experimentwise error rate      82 95
Tests of hypotheses, general linear hypotheses $H_0$: CB = O and $H_c$: CBM=O      295—297
Tests of hypotheses, H matrix      290 293 296
Tests of hypotheses, individual variables      80—83 95
Tests of hypotheses, individual variables, Bonferroni tests for      80—83 95
Tests of hypotheses, individual variables, Bonferroni tests for, modifications of      80—82
Tests of hypotheses, individual variables, Bonferroni tests for, protected tests      95
Tests of hypotheses, individual variables, Bonferroni tests for, simultaneous tests for      80 94
Tests of hypotheses, individual variables, Bonferroni tests for, table of critical values      78
Tests of hypotheses, Lawley — Hotelling test      292 295 296
Tests of hypotheses, likelihood ratio test      see “Wilks’ $\Lambda$”
Tests of hypotheses, likelihood ratio tests      see “Likelihood ratio test”
Tests of hypotheses, MANOVA      see “Multivariate analysis of variance mean vectors”
Tests of hypotheses, MANOVA, likelihood ratio test      71—72 91—92
Tests of hypotheses, Mests      see “t-tests”
Tests of hypotheses, nonparametric tests for several mean vectors      194
Tests of hypotheses, nonparametric tests for two mean vectors      113
Tests of hypotheses, overall regression test      289—293
Tests of hypotheses, overall regression test in terms of canonical correlations      323
Tests of hypotheses, paired observation test      97—99
Tests of hypotheses, partial F-test      110
Tests of hypotheses, power of tests      292—293
Tests of hypotheses, protected tests      95
Tests of hypotheses, robust versions of $T^2$-ests      114
Tests of hypotheses, simultaneous tests      80 94 146—148 150 274
Tests of hypotheses, stepdown test      110—111
Tests of hypotheses, union-intersection test      72—74
Total variance      8—9 341 382
Trace of a matrix      410
Transformation of a random variable, distribution of      38—40
Transformation of a random variable, distribution of, Jacobian      39
Two-sample test for mean vectors      87—92
Two-sample test for mean vectors, comparing mean vectors when $\Sigma_1\neq\Sigma_2$      100—104
Unbalanced data      152 155—160 168—174
Unbalanced data, contrasts      156—160
Unbalanced data, contrasts, Bonferroni confidence intervals      157
Unbalanced data, contrasts, simultaneous confidence intervals      156—157
Unbalanced data, discriminant functions      157
Unbalanced data, one-way model      155—160
Unbalanced data, tests on individual variables      157
Unbalanced data, two-way model      168—174
Unbalanced data, two-way model, constrained model      169—171
Univariate analysis of variance      see “Analysis of variance univariate”
Univariate normal distribution      37—38
Variables      see also “Random variables”
variables, categorical      2
Variables, commensurate      1
Variables, correlated      1
Variables, standardized      11
Variance inflation factor      21
Variance matrix      see “Covariance matrix”
Variance, generalized      8—9
Variance, population      3
Variance, sample      3
Variance, sample, unbiased      3
Variance, total      8 341 382
Variance-covariance matrix      see “Covariance matrix”
Varimax rotation      388
Vector(s), 0 vector      401
Vector(s), definition      399
Vector(s), differentiation      414—415
Vector(s), distance between two vectors      22—23
Vector(s), distance from origin      402
Vector(s), j vector      400
Vector(s), length of      402
Vector(s), linear independence and dependence of      406
Vector(s), normalized      402
Vector(s), orthogonal vectors      410
Vector(s), partitioned      12—14
Vector(s), product of      401—402
Vector(s), random      1 (see also “Random vectors”)
Vector(s), standardized vector      45
Vector(s), subvectors      12—14 (see also “Subvector(s)”)
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