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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
$T^2$-tests      60—120
$T^2$-tests and discriminant function      74 92 109
$T^2$-tests and F-distribution      67
$T^2$-tests and multivariate quality control      114—115
$T^2$-tests and quality control      114—115
$T^2$-tests for elliptically contoured distributions      112—113
$T^2$-tests on a sub vector      108—112
$T^2$-tests on a sub vector, covariates      110
$T^2$-tests, additional information, test for      108—112
$T^2$-tests, approximate tests, nonparametric tests      113
$T^2$-tests, approximate tests, when $\Sigma_1$, $\Sigma_2$      99—104
$T^2$-tests, Behrens — Fisher problem      99—104
$T^2$-tests, Behrens — Fisher problem, multivariate      100—104
$T^2$-tests, Behrens — Fisher problem, univariate      99—100
$T^2$-tests, degrees of freedom      65
$T^2$-tests, effect of each variable      67—70 87—91
$T^2$-tests, formal definition of $T^2$      66
$T^2$-tests, likelihood ratio test      71—72 91—92
$T^2$-tests, matched pairs      97—99
$T^2$-tests, one mean vector, $\Sigma$ known      60—61
$T^2$-tests, one mean vector, $\Sigma$ unknown      65—74
$T^2$-tests, paired observation test      97—99
$T^2$-tests, power      104—108
$T^2$-tests, power, tables      106 423—426
$T^2$-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      96—97
$T^2$-tests, robustness of $T^2$-tests to unequal covariance matrices      96
$T^2$-tests, selection of variables      111
$T^2$-tests, stepdown test      110—111
$T^2$-tests, table of critical values      419—420
$T^2$-tests, transformation to F      67
$T^2$-tests, two mean vectors, $\Sigma = \Sigma_2$      85—92
$T^2$-tests, two mean vectors, $\Sigma \neq \Sigma_2$      100—104
$T^2$-tests, union-intersection test      72—74 92
Additional information, test on      see “Tests of hypotheses on
Analysis of covariance      110 178—194
Analysis of covariance, multivariate      187—194
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      178—187
Analysis of covariance, univariate, assumptions      178—179
Analysis of covariance, univariate, one-way model      179—183
Analysis of covariance, univariate, two-way model      183—186 191
Analysis of covariance, univariate, unbalanced model      186—187
Analysis of variance, multivariate      see “Multivariate analysis of variance”
Analysis of variance, univariate (ANOVA), contrasts      142—145
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      144—145
Analysis of variance, univariate (ANOVA), unbalanced data      152—155 160—168
Analysis of variance, univariate (ANOVA), unbalanced data, cell means model      152 160—161
Analysis of variance, univariate (ANOVA), unbalanced data, contrasts      153—155 163—165
Analysis of variance, univariate (ANOVA), unbalanced data, one-way model      153—155
Analysis of variance, univariate (ANOVA), unbalanced data, two-way model      160—168
Analysis of variance, univariate (ANOVA), unbalanced data, two-way model, constrained model      165—168
anova      see “Analysis of variance univariate”
Apparent error rate      see “Error rate(s)”
Apple data      197
Association, measures of      289
Beetle data      118
Behrens — Fisher problem      99—104
Behrens — Fisher problem, multivariate      100—104
Behrens — Fisher problem, univariate      99—100
Biochemical data, full      199
Biochemical data, partial      192
Bonferroni critical values      78 144
Bonferroni critical values, table      421—422
Calcium data      69
Canonical correlation(s)      190 312—336
Canonical correlation(s) and discriminant analysis      312
Canonical correlation(s) and eigenvalues      314—316 323
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 “Canonical variates”
Canonical correlation(s), definition of      313
Canonical correlation(s), influence      333
Canonical correlation(s), properties of      317—320
Canonical correlation(s), redundancy analysis      331—333
Canonical correlation(s), redundancy analysis, robust estimators      333
Canonical correlation(s), singular value decomposition      315—316
Canonical correlation(s), tests of significance      320—326
Canonical correlation(s), tests of significance and test of overall regression      321 323
Canonical correlation(s), tests of significance, Lawley — Hotelling test      323
Canonical correlation(s), tests of significance, likelihood ratio test (Wilks’ A)      321—323
Canonical correlation(s), tests of significance, Pillai’s test      323
Canonical correlation(s), tests of significance, Roy’s test      323
Canonical correlation(s), tests of significance, subset of canonical correlations      324—326
Canonical correlation(s), tests of significance, test of independence      320—321
Canonical correlation(s), tests of significance, union-intersection test (Roy’s)      324
Canonical correlation(s), validation      326—327
Canonical correlation(s), validation, cross validation      326—327
Canonical correlation(s), validation, jackknife      327
Canonical variates      313 317—320 326—333
Canonical variates and eigenvectors      313—320 327
Canonical variates, canonical ridge weights      327
Canonical variates, common canonical variates      333
Canonical variates, definition of      313
Canonical variates, influence      333
Canonical variates, interpretation      328—331
Canonical variates, interpretation, correlations (structure coefficients)      329—331
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      331—333
Canonical variates, robust estimators      333
Canonical variates, scaling      317
Canonical variates, standardized coefficients      319
categorical data      255 262 266 306—307
Centering matrix      9—10
Central Limit Theorem (Multivariate)      53
Characteristic roots      see “Eigenvalues”
Chi-square distribution      48—49 53—54 60
Cholesky decomposition      42 408
Classification analysis (allocation)      230—265
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      240—247 (see also “Error rate(s)”)
Classification analysis (allocation), influence of individual observations      262
Classification analysis (allocation), logistic classification      254—259
Classification analysis (allocation), logistic classification for several groups      258
Classification analysis (allocation), logistic classification, comparison with linear classification      256—257
Classification analysis (allocation), logistic classification, quadratic logistic classification      258
Classification analysis (allocation), missing data      262—263
Classification analysis (allocation), nearest neighbor method      263
Classification analysis (allocation), posterior probabilities      234 236—237
Classification analysis (allocation), prior probabilities      230 236 238
Classification analysis (allocation), probit classification      259—261
Classification analysis (allocation), ridge classification      261
Classification analysis (allocation), robust classifications procedures      235
Classification analysis (allocation), several groups      236—239
Classification analysis (allocation), several groups, asymptotic optimality      236
Classification analysis (allocation), several groups, comparison of linear and quadratic rules      238—239
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      237—238
Classification analysis (allocation), several groups, regularized discriminant (classification) analysis      239
Classification analysis (allocation), subset selection      247—251
Classification analysis (allocation), subset selection with unequal covariance matrices      250—251
Classification analysis (allocation), subset selection, using error rates      249—250
Classification analysis (allocation), subset selection, using stepwise discriminant analysis      247—249
Classification analysis (allocation), subset selection, using stepwise discriminant analysis, bias      251—254
Classification analysis (allocation), two groups      230—235
Classification analysis (allocation), two groups, asymptotic optimality      232
Classification analysis (allocation), two groups, linear classification rule      231—232
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      232—233
Coefficient of determination      see “$R^2$”
Communality      see “Factor analysis communality”
Condition number      20
Confidence interval(s)      74—79
Confidence interval(s) for linear combination(s)      74 92—94
Confidence interval(s) for regression coefficients      273—274
Confidence interval(s), Bonferroni intervals      77—79 94
Confidence interval(s), simultaneous intervals      75—76 93—95
Confidence region for $\mu$      74
Confidence region for $\mu_1-\mu_2$      93
Constant density ellipsoid      40—41
Contaminated normal      28
Contour Plot      40—42
Contrast matrix      84 163 166 169—170
Contrast(s)      84 95 142—148 150—151 153—160
Contrast(s) with unbalanced data      153—160
Contrast(s), Bonferroni procedure      144
Contrast(s), orthogonal      144 154
Contrast(s), Scheffe procedure      144—145
Contrast(s), simultaneous      150
Correct classification rate      240
Correlation matrix and factor analysis      379—380 383 385—386 389 392
Correlation matrix and principal components      342 344—347 349 351 353—359 364 367—370
Correlation matrix as standardized covariance matrix      1
Correlation matrix of linear combinations of variables      16
Correlation matrix, bias      12
Correlation matrix, population      11—12
Correlation matrix, relationship to covariance matrix      11—12
Correlation matrix, sample      11
Correlation matrix, test comparing two covariance matrices      138—140
Correlation of two linear combinations      15
Correlation of two random variables      6
Correlation, bias      6
Correlation, canonical      see “Canonical correlation(s)”
Correspondence analysis      2 373
Covariance matrix (matrices) for one random vector      8—10
Covariance matrix (matrices) for two random vectors,      113
Covariance matrix (matrices), partitioned      12—13
Covariance matrix (matrices), pooled      87
Covariance matrix (matrices), population      10
Covariance matrix (matrices), positive definite      9—10
Covariance matrix (matrices), relationship to correlation matrix      11—12
Covariance matrix (matrices), sample      8—9
Covariance matrix (matrices), sample, distribution of      55
Covariance matrix (matrices), sample, unbiased      11
Covariance matrix (matrices), test for equality of      138—140
Covariance matrix (matrices), test for equality of table of critical values      446—447
Covariance of two linear combinations      15
Covariance of two random variables      5—6
Cross validation      244 326—327
Data matrix (Y)      7
Data, continuous      2
Data, discrete      2
Data, missing      23—27 (see also “Missing data”)
Density estimation      263
Density function      37—39
Determinant      409
Diabetes data      17
Diagonal matrix      11 400
Discriminant analysis (descriptive)      201—229 (see also “Discriminant function(s)”)
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      205—206
Discriminant analysis (descriptive), influence      206
Discriminant analysis (descriptive), ridge discriminant analysis      221—222
Discriminant analysis (descriptive), robust discriminant analysis      223—227
Discriminant analysis (descriptive), several groups      202—206
Discriminant analysis (descriptive), subset selection in higher order designs      218—219
Discriminant analysis (descriptive), subset selection, all possible subsets      218
Discriminant analysis (descriptive), subset selection, bias      219—221
Discriminant analysis (descriptive), subset selection, stepwise discriminant analysis      217—221
Discriminant analysis (descriptive), subset selection, using discriminant functions      217
Discriminant analysis (descriptive), tests of significance      207—210
Discriminant analysis (descriptive), two groups      201—202
Discriminant analysis (predictive)      see “Classification analysis”
Discriminant function(s) (descriptive)      see also “Discriminant analysis (descriptive)”
Discriminant function(s) (descriptive) for one group      74
Discriminant function(s) (descriptive) for two groups      92 201—202
Discriminant function(s) (descriptive) for two groups, effect of each variable      206—207
Discriminant function(s) (descriptive) for two groups, other estimators when $\Sigma$ is near singular      221—222
Discriminant function(s) (descriptive) for unbalanced data      157
Discriminant function(s) (descriptive), confidence intervals for      216
Discriminant function(s) (descriptive), interpretation of      210—215
Discriminant function(s) (descriptive), interpretation of correlations (structure coefficients)      211—215
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      221—222
Discriminant function(s) (descriptive), robust discriminant functions      223—227
Discriminant function(s) (descriptive), robust discriminant functions, for several groups (MANOVA)      128 151 202—206
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      206—207
Dispersion matrix      see “Covariance matrix”
Distance between two vectors (Mahalanobis)      22—23
E matrix      122 203
Eigenvalues      411—414
Eigenvalues and canonical correlations      314—316 323
Eigenvalues and discriminant functions      128 203—205 209 212—215 222—226
Eigenvalues and factor analysis      381—383
Eigenvalues and MANOVA      111
Eigenvalues and principal components      338 341
Eigenvectors      411—414
Eigenvectors and discriminant functions      203—204 210 212—213 222—225
Eigenvectors and factor analysis      381
Eigenvectors and principal components      338
Ellipsoid, constant density      40—41
Elliptically contoured distributions      56 112—113
EM algorithm      25—26
Error rate(s)      240—247
Error rate(s), actual error rate      240
Error rate(s), apparent correct classification rate      243—245
Error rate(s), apparent error rate      243—245
Error rate(s), apparent error rate, bias, correction for      244—247
Error rate(s), apparent error rate, bootstrap estimator      245
Error rate(s), apparent error rate, comparison of methods      245—247
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      240—242
Error rate(s), plug-in estimator of error rate      240—243
Error rate(s), resubstitution      243
Error rate(s), true error rate      240
Estimation, least squares      267—268 281—282
Estimation, likelihood function      49
Estimation, maximum likelihood      49—52
Estimator, least squares      267—268 281—282
Estimator, maximum likelihood      49—52
Estimator, unbiased      2—3
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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