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Rencher A.C. — Methods of multivariate analysis

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Название: Methods of multivariate analysis

Автор: Rencher A.C.

Аннотация:

This textbook extends univariate procedures with one dependent variable to analogous multivariate techniques involving several dependent variables, and finds functions of variables that discriminate among groups in the data and that reveal the basic dimensionality and characteristic patterns of the data. The second edition adds two chapters on cluster analysis and graphical techniques.

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2002

Количество страниц: 732

Добавлена в каталог: 08.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Growth curves, one sample      221—229
Growth curves, orthogonal polynomials      222—225
Growth curves, polynomial function of t      225—227
Growth curves, several samples      229—230
Growth curves, unequally spaced time points      225—227
Guinea pig data      201
H matrix      160—161 343—344
Height-weight data      45
Hematology data      109—110
Hierarchical clustering      see Cluster analysis hierarchical
Hotelling — Lawley test statistic      see Lawley — Hotelling test statistic
Hotelling's -statistic      see $T^2$

-statistic
Hyperellipsoid      73
Hypothesis tests      see Tests of hypotheses
Identity matrix      8
Imputation      74
Independence of variables, test for      265—266
Independence of variables, test for, table of exact critical values      590
Indicator variables      see Dummy variables
Inferential statistics      2
Intra-class correlation      198—199
Kernel density estimators      315—317
kurtosis      94—95 98—99 103—104
Largest root test      see Roy's test statistic
Latent roots      see Eigenvalues
Lawley — Hotelling test statistic: definition of      167
Lawley — Hotelling test statistic: table of critical values      582—586
Length of vector      14
Likelihood function      90
Likelihood ratio test(s): for covariance matrices      248—250 253 256 260 262 265
Likelihood ratio test(s): for mean vectors      126 164
Likelihood ratio test(s): in factor analysis      428
Linear classification functions      301—306
Linear combination of matrices      19
Linear combination of vectors      19
Linear combination(s) of variables      2 67—73 113
Linear combination(s) of variables, correlation matrix for several linear combinations      72
Linear combination(s) of variables, correlation of two linear combinations      67 71—73
Linear combination(s) of variables, covariance matrix for several linear combinations      69—70 72—73
Linear combination(s) of variables, covariance of two linear combinations      67—68 71—72
Linear combination(s) of variables, distribution of      86
Linear combination(s) of variables, mean of a single linear combination      67 71—72
Linear combination(s) of variables, mean vector for several linear combinations      69
Linear combination(s) of variables, variance of a single linear combination      67 71—72
Linear hypotheses      141—142 199—201 208—225
Mahalanobis distance      76—77 83
Mandible data      247
Manova      130 158. multivariate
Matrix (matrices): algebra of      5—37
Matrix (matrices): bilinear form      19—20
Matrix (matrices): Burt matrix      526—529
Matrix (matrices): Cholesky decomposition      25—26
Matrix (matrices): conformable      11
Matrix (matrices): covariance matrix      57—59
Matrix (matrices): definition      5—6
Matrix (matrices): determinant      26—29 34.
Matrix (matrices): determinant of diagonal matrix      27
Matrix (matrices): determinant of inverse matrix      29
Matrix (matrices): determinant of partitioned matrix      29
Matrix (matrices): determinant of positive definite matrix      28
Matrix (matrices): determinant of product      28
Matrix (matrices): determinant of scalar multiple of a matrix      28
Matrix (matrices): determinant of singular matrix      28
Matrix (matrices): determinant of transpose      29
Matrix (matrices): diagonal      8
Matrix (matrices): eigenvalues      32—37. See also Eigenvalues
Matrix (matrices): eigenvalues and determinant      34
Matrix (matrices): eigenvalues and trace      34
Matrix (matrices): eigenvalues of I+A      33
Matrix (matrices): eigenvalues of inverse matrix      36
Matrix (matrices): eigenvalues of positive definite matrix      34
Matrix (matrices): eigenvalues of positive definite matrix, Perron — Frobenius theorem      34
Matrix (matrices): eigenvalues of positive definite matrix, square root matrix      36
Matrix (matrices): eigenvalues of product      35
Matrix (matrices): eigenvalues of square matrix      36
Matrix (matrices): eigenvalues of symmetric matrix      35
Matrix (matrices): eigenvalues of symmetric matrix, spectral decomposition      35
Matrix (matrices): eigenvalues, characteristic equation      32
Matrix (matrices): eigenvalues, singular value decomposition      36
Matrix (matrices): eigenvectors      32—37. See also Eigenvectors
Matrix (matrices): equality of      7
Matrix (matrices): identity      8
Matrix (matrices): indicator matrix      526—527
Matrix (matrices): inverse      23—25
Matrix (matrices): inverse of partitioned matrix      25
Matrix (matrices): inverse of product      24
Matrix (matrices): inverse of transpose      24
Matrix (matrices): J matrix      9
Matrix (matrices): j vector      9
Matrix (matrices): linear combination of      19
Matrix (matrices): nonsingular matrix      23
Matrix (matrices): notation for matrix and vector      5—6
Matrix (matrices): O (zero matrix)      9
Matrix (matrices): operations with      9—20
Matrix (matrices): operations with distributive law      12
Matrix (matrices): operations with factoring      12—13 15
Matrix (matrices): operations with product      11—20 23—25
Matrix (matrices): operations with product and eigenvalues      34—35
Matrix (matrices): operations with product of matrix and scalar      19
Matrix (matrices): operations with product of matrix and transpose      16—18
Matrix (matrices): operations with product of matrix and vector      12—13 16 21
Matrix (matrices): operations with product of matrix and vector as linear combination      21
Matrix (matrices): operations with product of vectors      14
Matrix (matrices): operations with product, conformable      11
Matrix (matrices): operations with product, distributive over addition      12
Matrix (matrices): operations with product, noncommutativity of      11
Matrix (matrices): operations with product, product equal zero      23
Matrix (matrices): operations with product, transpose of      12
Matrix (matrices): operations with product, triple product      13
Matrix (matrices): operations with product, with diagonal matrix      18
Matrix (matrices): operations with sum      10
Matrix (matrices): operations with sum, commutativity of      10
Matrix (matrices): orthogonal      31
Matrix (matrices): orthogonal, rotation of axes      31—32
Matrix (matrices): partitioned matrices      20—22
Matrix (matrices): partitioned matrices, determinant of      29
Matrix (matrices): partitioned matrices, inverse of      25
Matrix (matrices): partitioned matrices, product of      20—21
Matrix (matrices): partitioned matrices, transpose of      22
Matrix (matrices): Perron — Frobenius theorem      34 402
Matrix (matrices): positive definite      25 34
Matrix (matrices): positive semidefinite      25 34
Matrix (matrices): quadratic form      19
Matrix (matrices): rank      22—23
Matrix (matrices): rank, full rank      22
Matrix (matrices): scalar      6
Matrix (matrices): scalar, product of scalar and matrix      19
Matrix (matrices): singular matrix      24
Matrix (matrices): singular value decomposition      36
Matrix (matrices): size of a matrix      6
Matrix (matrices): spectral decomposition      35
Matrix (matrices): square root matrix      36
Matrix (matrices): sum of products in vector notation      14
Matrix (matrices): sum of squares in vector notation      14
Matrix (matrices): symmetric      7 35
Matrix (matrices): trace      30 34 69
Matrix (matrices): trace and eigenvalues      34
Matrix (matrices): trace of product      30
Matrix (matrices): trace of sum      30
Matrix (matrices): transpose      6—7
Matrix (matrices): transpose of product      12
Matrix (matrices): transpose of sum      10
Matrix (matrices): triangular      8
Matrix (matrices): vectors      see Vector(s)
Matrix (matrices): zero matrix (O) and zero vector (0)      9
Maximum Likelihood Estimation      90—91
Maximum likelihood estimation of correlation matrix      91
Maximum likelihood estimation of covariance matrix      90
Maximum likelihood estimation of mean vector      90—91
Maximum likelihood estimation, likelihood function      90

Maximum likelihood estimation, multivariate normal      90
Mean vector      54—56 83 90—92
Mean vector, notation      54
Mean vector, population mean vector $(\mu)$       55—56
Mean vector, sample mean vector $(\bar{y})$       54—56
Mean vector, sample mean vector $(\bar{y})$ and sample covariance matrix, independence of      92
Mean vector, sample mean vector $(\bar{y})$ from data matrix      55
Mean vector, sample mean vector $(\bar{y})$ , distribution of      91
Mean: geometric      174
Mean: of linear function      67 72
Mean: of product      46
Mean: of sum      46
Mean: population mean $(\mu)$       43
Mean: sample mean $(\bar{y})$       43—44
Measurement scale      2
Measurement scale, interval scale      2
Measurement scale, ordinal scale      2
Measurement scale, ratio scale      2
Mice data      241
Misclassification rates      see Error rate(s)
Missing values      74—76
Multicollinearity      74 84
Multidimensional scaling      504—514
Multidimensional scaling, classical solution      see Metric multidimensional scaling
Multidimensional scaling, definition      504—505
Multidimensional scaling, distances      504—505
Multidimensional scaling, distances, seriation (ranking)      504
Multidimensional scaling, metric multidimensional scaling      504—508
Multidimensional scaling, metric multidimensional scaling and principal component analysis      506
Multidimensional scaling, metric multidimensional scaling, algorithm for finding the points      505—508
Multidimensional scaling, nonmetric multidimensional scaling      505 508—514
Multidimensional scaling, nonmetric multidimensional scaling, monotonic regression      509—510
Multidimensional scaling, nonmetric multidimensional scaling, ranked dissimilarities      508—509
Multidimensional scaling, nonmetric multidimensional scaling, STRESS      510—512
Multidimensional scaling, principal coordinate analysis      see Metric multidimensional scaling
Multidimensional scaling, spectral decomposition      505—506
Multiple correlation      332 361—362 423.
Multiple correspondence analysis      526—530
Multiple correspondence analysis, Burt matrix      526—529
Multiple correspondence analysis, column coordinates      527 529—530
Multiple correspondence analysis, indicator matrix      526—527
Multiple regression      see Regression multiple
Multivariate analysis      1
Multivariate analysis of variance (Manova)      see Analysis of variance multivariate
Multivariate analysis, descriptive statistics      1—2
Multivariate analysis, inferential statistics      2
Multivariate data: basic types of      4
Multivariate data: plotting of      52—53
Multivariate data: sparceness of      97
Multivariate inference      2
Multivariate normal distribution      82—105
Multivariate normal distribution, applicability of      85
Multivariate normal distribution, conditional distribution      88
Multivariate normal distribution, contour plots      84—85
Multivariate normal distribution, density function      83
Multivariate normal distribution, distribution of $\bar{y}$ and S      91—92
Multivariate normal distribution, features of      82
Multivariate normal distribution, independence of $\bar{y}$ and S      92
Multivariate normal distribution, linear combinations of      86
Multivariate normal distribution, marginal distribution      87
Multivariate normal distribution, maximum likelihood estimates      90—91. See also Maximum likelihood estimation
Multivariate normal distribution, properties of      85—90
Multivariate normal distribution, quadratic form and chi-square distribution      86
Multivariate normal distribution, standardized variables      86
Multivariate normal distribution, zero covariance matrix implies independence of subvectors      87
Multivariate normality, dynamic plot      98
Multivariate normality, scatter plots      98 105
Multivariate normality, skewness and kurtosis, multivariate      98—99 103—104 106
Multivariate normality, skewness and kurtosis, table of critical values      553—556
Multivariate normality, tests for      92 96—99
Multivariate normality, tests for       97—98 102—103
Multivariate normality, tests for and chi-square      98
Multivariate normality, tests for table of critical values      557
Multivariate regression      see Regression multivariate
Nonsingular matrix      23
Normal distribution: bivariate normal      46 84 88—89 133
Normal distribution: multivariate normal      see Multivariate normal distribution
Normal distribution: univariate normal      82—83 86
Normality, tests for      see Multivariate normality; Univariate normality
Norway crime data      544
Numerical taxonomy      see Cluster analysis
Objectives of this book      3
Observations      1
One-sample test for a mean vector      117—121
Orthogonal matrix      31
Orthogonal polynomials      222—225
Orthogonal polynomials, table of      587
Orthogonal vectors      50
Outliers: multivariate: kurtosis      103—104
Outliers: multivariate: kurtosis, elliptically symmetric distributions      103
Outliers: multivariate: principal components      389—392
Outliers: multivariate: slippage in mean, variance, and correlation      101
Outliers: multivariate: Wilks' statistic      102—103
Outliers: univariate: accommodation      100
Outliers: univariate: block test      101
Outliers: univariate: identification      100
Outliers: univariate: masking      101
Outliers: univariate: maximum studentized residual      100—101
Outliers: univariate: skewness and kurtosis      101
Outliers: univariate: slippage in mean and variance      100
Outliers: univariate: swamping      101
Overall variability      73—74
Paired observation test      132—136
Partial F-tests      127 138 232 293—296
Partitioned matrices      see Matrix (matrices) partitioned
Partitioning      see Cluster analysis partitioning
Pattern recognition      see Cluster analysis
People data      526
Perception data      419
Perron — Frobenius theorem      34 402
Pillai's test statistic: definition of      166
Pillai's test statistic: table of critical values      578—581
Piston ring data      518
Plasma data      246
Plotting multivariate data      52—53
Politics data      542
Positive definite matrix      25
Positive definite matrix, positive definite sample covariance matrix      67
Prerequisites for this book      3
Principal components      380—407
Principal components and biplots      531—532
Principal components and cluster analysis      390—393 395 482—484 487
Principal components and factor analysis      403 408—409 447—448
Principal components and perpendicular regression      385 387—389
Principal components as rotation of axes      381—382 384—385
Principal components from S or R      383—384 393—397
Principal components from S or R, nonuniqueness of components from R      397
Principal components, algebra of      385—387
Principal components, component scores      386
Principal components, definition of      380 382 385
Principal components, dimension reduction      381—384 385—387 389
Principal components, eigenvalues and eigenvectors      382—385 397—398
Principal components, eigenvalues and eigenvectors, major axis      384 388
Principal components, geometry of      381—385
Principal components, interpretation      401—404
Principal components, interpretation, correlations      403—404
Principal components, interpretation, rotation      403
Principal components, interpretation, special patterns in S or R      401—403
Principal components, interpretation, special patterns in S or R, size and shape      402—403
Principal components, large variance of a variable, effect of      383—384 402
Principal components, last few principal components      382 389 401
Principal components, maximum variance      380 385
Principal components, minimum perpendicular distances to line      387—388
Principal components, number of components to retain      397—401
Principal components, orthogonality of      380 383—384
Principal components, percent of variance      383 397
Principal components, plotting of      389—393
Principal components, plotting of assessing normality      389—390
Principal components, plotting of detection of outliers      389—391
Principal components, properties of      381—386

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