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

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Ќазвание: Multivariate Statistical Inference and Applications

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

јннотаци€:

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: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1997

 оличество страниц: 592

ƒобавлена в каталог: 12.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$T^2$-tests      60Ч120
$T^2$-tests and discriminant function      74 92 109
$T^2$-tests and F-distribution      67
$T^2$-tests and multivariate quality control      114Ч115
$T^2$-tests and quality control      114Ч115
$T^2$-tests for elliptically contoured distributions      112Ч113
$T^2$-tests on a sub vector      108Ч112
$T^2$-tests on a sub vector, covariates      110
$T^2$-tests, additional information, test for      108Ч112
$T^2$-tests, approximate tests, nonparametric tests      113
$T^2$-tests, approximate tests, when $\Sigma_1$, $\Sigma_2$      99Ч104
$T^2$-tests, Behrens Ч Fisher problem      99Ч104
$T^2$-tests, Behrens Ч Fisher problem, multivariate      100Ч104
$T^2$-tests, Behrens Ч Fisher problem, univariate      99Ч100
$T^2$-tests, degrees of freedom      65
$T^2$-tests, effect of each variable      67Ч70 87Ч91
$T^2$-tests, formal definition of $T^2$      66
$T^2$-tests, likelihood ratio test      71Ч72 91Ч92
$T^2$-tests, matched pairs      97Ч99
$T^2$-tests, one mean vector, $\Sigma$ known      60Ч61
$T^2$-tests, one mean vector, $\Sigma$ unknown      65Ч74
$T^2$-tests, paired observation test      97Ч99
$T^2$-tests, power      104Ч108
$T^2$-tests, power, tables      106 423Ч426
$T^2$-tests, properties of      70 91
$T^2$-tests, robust versions of $T^2$-ests      114
$T^2$-tests, robustness of $T^2$-tests to nonnormality      96Ч97
$T^2$-tests, robustness of $T^2$-tests to unequal covariance matrices      96
$T^2$-tests, selection of variables      111
$T^2$-tests, stepdown test      110Ч111
$T^2$-tests, table of critical values      419Ч420
$T^2$-tests, transformation to F      67
$T^2$-tests, two mean vectors, $\Sigma = \Sigma_2$      85Ч92
$T^2$-tests, two mean vectors, $\Sigma \neq \Sigma_2$      100Ч104
$T^2$-tests, union-intersection test      72Ч74 92
Additional information, test on      see УTests of hypotheses on
Analysis of covariance      110 178Ч194
Analysis of covariance, multivariate      187Ч194
Analysis of covariance, multivariate and canonical correlations      190
Analysis of covariance, multivariate, one-way model      187
Analysis of covariance, multivariate, two-way model      188
Analysis of covariance, univariate      178Ч187
Analysis of covariance, univariate, assumptions      178Ч179
Analysis of covariance, univariate, one-way model      179Ч183
Analysis of covariance, univariate, two-way model      183Ч186 191
Analysis of covariance, univariate, unbalanced model      186Ч187
Analysis of variance, multivariate      see УMultivariate analysis of varianceФ
Analysis of variance, univariate (ANOVA), contrasts      142Ч145
Analysis of variance, univariate (ANOVA), contrasts, Bonferroni procedure      144
Analysis of variance, univariate (ANOVA), contrasts, orthogonal      144
Analysis of variance, univariate (ANOVA), contrasts, Scheffe procedure      144Ч145
Analysis of variance, univariate (ANOVA), unbalanced data      152Ч155 160Ч168
Analysis of variance, univariate (ANOVA), unbalanced data, cell means model      152 160Ч161
Analysis of variance, univariate (ANOVA), unbalanced data, contrasts      153Ч155 163Ч165
Analysis of variance, univariate (ANOVA), unbalanced data, one-way model      153Ч155
Analysis of variance, univariate (ANOVA), unbalanced data, two-way model      160Ч168
Analysis of variance, univariate (ANOVA), unbalanced data, two-way model, constrained model      165Ч168
anova      see УAnalysis of variance univariateФ
Apparent error rate      see УError rate(s)Ф
Apple data      197
Association, measures of      289
Beetle data      118
Behrens Ч Fisher problem      99Ч104
Behrens Ч Fisher problem, multivariate      100Ч104
Behrens Ч Fisher problem, univariate      99Ч100
Biochemical data, full      199
Biochemical data, partial      192
Bonferroni critical values      78 144
Bonferroni critical values, table      421Ч422
Calcium data      69
Canonical correlation(s)      190 312Ч336
Canonical correlation(s) and discriminant analysis      312
Canonical correlation(s) and eigenvalues      314Ч316 323
Canonical correlation(s) and MANOVA      312 333
Canonical correlation(s) and measures of association      289
Canonical correlation(s) and multiple correlation      314 319
Canonical correlation(s), canonical variates      see УCanonical variatesФ
Canonical correlation(s), definition of      313
Canonical correlation(s), influence      333
Canonical correlation(s), properties of      317Ч320
Canonical correlation(s), redundancy analysis      331Ч333
Canonical correlation(s), redundancy analysis, robust estimators      333
Canonical correlation(s), singular value decomposition      315Ч316
Canonical correlation(s), tests of significance      320Ч326
Canonical correlation(s), tests of significance and test of overall regression      321 323
Canonical correlation(s), tests of significance, Lawley Ч Hotelling test      323
Canonical correlation(s), tests of significance, likelihood ratio test (WilksТ A)      321Ч323
Canonical correlation(s), tests of significance, PillaiТs test      323
Canonical correlation(s), tests of significance, RoyТs test      323
Canonical correlation(s), tests of significance, subset of canonical correlations      324Ч326
Canonical correlation(s), tests of significance, test of independence      320Ч321
Canonical correlation(s), tests of significance, union-intersection test (RoyТs)      324
Canonical correlation(s), validation      326Ч327
Canonical correlation(s), validation, cross validation      326Ч327
Canonical correlation(s), validation, jackknife      327
Canonical variates      313 317Ч320 326Ч333
Canonical variates and eigenvectors      313Ч320 327
Canonical variates, canonical ridge weights      327
Canonical variates, common canonical variates      333
Canonical variates, definition of      313
Canonical variates, influence      333
Canonical variates, interpretation      328Ч331
Canonical variates, interpretation, correlations (structure coefficients)      329Ч331
Canonical variates, interpretation, rotation      328
Canonical variates, interpretation, standardized coefficients      328
Canonical variates, nonlinear canonical variates      333
Canonical variates, properties of      320
Canonical variates, redundancy analysis      331Ч333
Canonical variates, robust estimators      333
Canonical variates, scaling      317
Canonical variates, standardized coefficients      319
categorical data      255 262 266 306Ч307
Centering matrix      9Ч10
Central Limit Theorem (Multivariate)      53
Characteristic roots      see УEigenvaluesФ
Chi-square distribution      48Ч49 53Ч54 60
Cholesky decomposition      42 408
Classification analysis (allocation)      230Ч265
Classification analysis (allocation) and discriminant analysis      201
Classification analysis (allocation) for categorical data      262
Classification analysis (allocation), assigning a sampling unit to a group      230
Classification analysis (allocation), assumptions      234
Classification analysis (allocation), assumptions, robustness to departures from      234
Classification analysis (allocation), correct classification rates      240
Classification analysis (allocation), costs of misclassification      233
Classification analysis (allocation), density estimation      263
Classification analysis (allocation), discriminant functions used in classification      232 239
Classification analysis (allocation), error rates      240Ч247 (see also УError rate(s)Ф)
Classification analysis (allocation), influence of individual observations      262
Classification analysis (allocation), logistic classification      254Ч259
Classification analysis (allocation), logistic classification for several groups      258
Classification analysis (allocation), logistic classification, comparison with linear classification      256Ч257
Classification analysis (allocation), logistic classification, quadratic logistic classification      258
Classification analysis (allocation), missing data      262Ч263
Classification analysis (allocation), nearest neighbor method      263
Classification analysis (allocation), posterior probabilities      234 236Ч237
Classification analysis (allocation), prior probabilities      230 236 238
Classification analysis (allocation), probit classification      259Ч261
Classification analysis (allocation), ridge classification      261
Classification analysis (allocation), robust classifications procedures      235
Classification analysis (allocation), several groups      236Ч239
Classification analysis (allocation), several groups, asymptotic optimality      236
Classification analysis (allocation), several groups, comparison of linear and quadratic rules      238Ч239
Classification analysis (allocation), several groups, linear classification function      236
Classification analysis (allocation), several groups, maximum likelihood rule      236
Classification analysis (allocation), several groups, optimal classification rule      236
Classification analysis (allocation), several groups, quadratic classification function      237Ч238
Classification analysis (allocation), several groups, regularized discriminant (classification) analysis      239
Classification analysis (allocation), subset selection      247Ч251
Classification analysis (allocation), subset selection with unequal covariance matrices      250Ч251
Classification analysis (allocation), subset selection, using error rates      249Ч250
Classification analysis (allocation), subset selection, using stepwise discriminant analysis      247Ч249
Classification analysis (allocation), subset selection, using stepwise discriminant analysis, bias      251Ч254
Classification analysis (allocation), two groups      230Ч235
Classification analysis (allocation), two groups, asymptotic optimality      232
Classification analysis (allocation), two groups, linear classification rule      231Ч232
Classification analysis (allocation), two groups, maximum likelihood rule      230
Classification analysis (allocation), two groups, optimal classification rule      230
Classification analysis (allocation), two groups, quadratic classification rule      232Ч233
Coefficient of determination      see У$R^2$Ф
Communality      see УFactor analysis communalityФ
Condition number      20
Confidence interval(s)      74Ч79
Confidence interval(s) for linear combination(s)      74 92Ч94
Confidence interval(s) for regression coefficients      273Ч274
Confidence interval(s), Bonferroni intervals      77Ч79 94
Confidence interval(s), simultaneous intervals      75Ч76 93Ч95
Confidence region for $\mu$      74
Confidence region for $\mu_1-\mu_2$      93
Constant density ellipsoid      40Ч41
Contaminated normal      28
Contour Plot      40Ч42
Contrast matrix      84 163 166 169Ч170
Contrast(s)      84 95 142Ч148 150Ч151 153Ч160
Contrast(s) with unbalanced data      153Ч160
Contrast(s), Bonferroni procedure      144
Contrast(s), orthogonal      144 154
Contrast(s), Scheffe procedure      144Ч145
Contrast(s), simultaneous      150
Correct classification rate      240
Correlation matrix and factor analysis      379Ч380 383 385Ч386 389 392
Correlation matrix and principal components      342 344Ч347 349 351 353Ч359 364 367Ч370
Correlation matrix as standardized covariance matrix      1
Correlation matrix of linear combinations of variables      16
Correlation matrix, bias      12
Correlation matrix, population      11Ч12
Correlation matrix, relationship to covariance matrix      11Ч12
Correlation matrix, sample      11
Correlation matrix, test comparing two covariance matrices      138Ч140
Correlation of two linear combinations      15
Correlation of two random variables      6
Correlation, bias      6
Correlation, canonical      see УCanonical correlation(s)Ф
Correspondence analysis      2 373
Covariance matrix (matrices) for one random vector      8Ч10
Covariance matrix (matrices) for two random vectors,      113
Covariance matrix (matrices), partitioned      12Ч13
Covariance matrix (matrices), pooled      87
Covariance matrix (matrices), population      10
Covariance matrix (matrices), positive definite      9Ч10
Covariance matrix (matrices), relationship to correlation matrix      11Ч12
Covariance matrix (matrices), sample      8Ч9
Covariance matrix (matrices), sample, distribution of      55
Covariance matrix (matrices), sample, unbiased      11
Covariance matrix (matrices), test for equality of      138Ч140
Covariance matrix (matrices), test for equality of table of critical values      446Ч447
Covariance of two linear combinations      15
Covariance of two random variables      5Ч6
Cross validation      244 326Ч327
Data matrix (Y)      7
Data, continuous      2
Data, discrete      2
Data, missing      23Ч27 (see also УMissing dataФ)
Density estimation      263
Density function      37Ч39
Determinant      409
Diabetes data      17
Diagonal matrix      11 400
Discriminant analysis (descriptive)      201Ч229 (see also УDiscriminant function(s)Ф)
Discriminant analysis (descriptive) and canonical correlation      312
Discriminant analysis (descriptive) and classification analysis      201
Discriminant analysis (descriptive) for two-way designs      210
Discriminant analysis (descriptive), assumptions      205Ч206
Discriminant analysis (descriptive), influence      206
Discriminant analysis (descriptive), ridge discriminant analysis      221Ч222
Discriminant analysis (descriptive), robust discriminant analysis      223Ч227
Discriminant analysis (descriptive), several groups      202Ч206
Discriminant analysis (descriptive), subset selection in higher order designs      218Ч219
Discriminant analysis (descriptive), subset selection, all possible subsets      218
Discriminant analysis (descriptive), subset selection, bias      219Ч221
Discriminant analysis (descriptive), subset selection, stepwise discriminant analysis      217Ч221
Discriminant analysis (descriptive), subset selection, using discriminant functions      217
Discriminant analysis (descriptive), tests of significance      207Ч210
Discriminant analysis (descriptive), two groups      201Ч202
Discriminant analysis (predictive)      see УClassification analysisФ
Discriminant function(s) (descriptive)      see also УDiscriminant analysis (descriptive)Ф
Discriminant function(s) (descriptive) for one group      74
Discriminant function(s) (descriptive) for two groups      92 201Ч202
Discriminant function(s) (descriptive) for two groups, effect of each variable      206Ч207
Discriminant function(s) (descriptive) for two groups, other estimators when $\Sigma$ is near singular      221Ч222
Discriminant function(s) (descriptive) for unbalanced data      157
Discriminant function(s) (descriptive), confidence intervals for      216
Discriminant function(s) (descriptive), interpretation of      210Ч215
Discriminant function(s) (descriptive), interpretation of correlations (structure coefficients)      211Ч215
Discriminant function(s) (descriptive), interpretation of partial F-tests      211
Discriminant function(s) (descriptive), interpretation of standardized coefficients      211
Discriminant function(s) (descriptive), invariance of      202
Discriminant function(s) (descriptive), plotting      216
Discriminant function(s) (descriptive), ridge estimator      221Ч222
Discriminant function(s) (descriptive), robust discriminant functions      223Ч227
Discriminant function(s) (descriptive), robust discriminant functions, for several groups (MANOVA)      128 151 202Ч206
Discriminant function(s) (descriptive), robust discriminant functions, other estimators when $\Sigma$ is near singular      222
Discriminant function(s) (descriptive), robust discriminant functions, properties      203
Discriminant function(s) (descriptive), standardized coefficients      206Ч207
Dispersion matrix      see УCovariance matrixФ
Distance between two vectors (Mahalanobis)      22Ч23
E matrix      122 203
Eigenvalues      411Ч414
Eigenvalues and canonical correlations      314Ч316 323
Eigenvalues and discriminant functions      128 203Ч205 209 212Ч215 222Ч226
Eigenvalues and factor analysis      381Ч383
Eigenvalues and MANOVA      111
Eigenvalues and principal components      338 341
Eigenvectors      411Ч414
Eigenvectors and discriminant functions      203Ч204 210 212Ч213 222Ч225
Eigenvectors and factor analysis      381
Eigenvectors and principal components      338
Ellipsoid, constant density      40Ч41
Elliptically contoured distributions      56 112Ч113
EM algorithm      25Ч26
Error rate(s)      240Ч247
Error rate(s), actual error rate      240
Error rate(s), apparent correct classification rate      243Ч245
Error rate(s), apparent error rate      243Ч245
Error rate(s), apparent error rate, bias, correction for      244Ч247
Error rate(s), apparent error rate, bootstrap estimator      245
Error rate(s), apparent error rate, comparison of methods      245Ч247
Error rate(s), apparent error rate, cross validation      244
Error rate(s), apparent error rate, holdout method      244
Error rate(s), apparent error rate, leaving-one-out-method      244
Error rate(s), conditional error rate      240
Error rate(s), expected actual error rate      240
Error rate(s), experimentwise      2 82 95
Error rate(s), maximum likelihood estimator of      242
Error rate(s), optimum error rate      240Ч242
Error rate(s), plug-in estimator of error rate      240Ч243
Error rate(s), resubstitution      243
Error rate(s), true error rate      240
Estimation, least squares      267Ч268 281Ч282
Estimation, likelihood function      49
Estimation, maximum likelihood      49Ч52
Estimator, least squares      267Ч268 281Ч282
Estimator, maximum likelihood      49Ч52
Estimator, unbiased      2Ч3
Expected value of random matrix      10
Expected value of random vector [E(y)]      8
Expected value of sample covariance $[E(s_{xy})]$      6
Expected value of sample covariance matrix [F(S)]      11
Expected value of sample mean $[E(\bar{y})]$      2
Expected value of sample mean vector $[E(\bar{y})]$      8
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