Multivariate statistical analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XVIII, 549 S. graph. Darst. |
| ISBN: | 9812791752 9789812791757 |
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| 008 | 081201s2009 d||| |||| 00||| eng d | ||
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| 020 | |a 9812791752 |c (hbk.) : £49.00 |9 981-279-175-2 | ||
| 020 | |a 9789812791757 |9 978-981-279-175-7 | ||
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| 084 | |a MAT 627f |2 stub | ||
| 100 | 1 | |a Mukhopadhyay, Parimal |e Verfasser |0 (DE-588)170031993 |4 aut | |
| 245 | 1 | 0 | |a Multivariate statistical analysis |c Parimal Mukhopadhyay |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2009 | |
| 300 | |a XVIII, 549 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Multivariate analysis | |
| 650 | 0 | 7 | |a Multivariate Analyse |0 (DE-588)4040708-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994330&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
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| _version_ | 1804138364198191105 |
|---|---|
| adam_text | Multivariate
Statistical Analysis
This textbook presents a classical approach to some techniques of
multivariate analysis in a simple and transparent manner. It offers
clear and concise development of the concepts; interpretation
of the output of the analysis; and criteria for selection of the
methods, taking into account the strengths and weaknesses of
each. With its roots in matrix algebra, for which a separate
chapter has been added as an appendix, the book includes both
data-oriented techniques and a reasonable coverage of classical
methods supplemented by comments about robustness and
general practical applicability. It also illustrates the methods of
numerical calculations at various stages.
This self-contained book is ¡deal as an advanced textbook for
graduate students in statistics and other disciplines like social,
biological and physical sciences. It will also be of benefit to
professional statisticians.
The author
¡s a
former Professor of the Indian Statistical Institute, India.
Contents
Preface
vii
Introduction
1-2
1:
Preliminaries
3-8
1.1
Introduction
3
1.2
Outline of Multivariate Methods
5
1.2.1
Dependence methods
6
1.2.2
Interdependence analysis
7
2:
Organization of Multivariate Data
9-41
2.1
Introduction
9
2.2
The Data Matrix
9
2.3
Summary Statistics
11
2.4
Linear Combination of Variables
18
2.5
Some Important Linear Transformations
20
2.6
Expectation and Covariance of Random Vectors
22
2.7
Expectation and Variance of Quadratic Forms of
Random Variables
25
2.8
Measures of Distance
27
2.9
Missing Observations
31
2.10
Exercises and Complements
34
2.11
Appendix
41
xjj Contents
3:
Multivariate
Normal Distributions and
Related Distributions
43 - 100
3.1
Introduction
43
3.2
Multivariate Normal Distribution
43
3.3
Transformation of Normal Data Matrix
58
3.4
Some Results on Quadratic Forms
60
3.5
Multivariate Central Limit Theorem
64
3.6
Maximum Likelihood Estimation of Parameters
68
3.6.1
Multivariate normal likelihood
69
3.6.2
Maximum likelihood estimation
70
3.7
Matrix Normal Distribution
77
3.8
The Multivariate
t
Distribution
77
3.9
The Dirichlet Distribution
78
3.10
Multivariate Skewness and Kurtosis
80
3.11
Examining the Assumption of Normality
81
3.11.1
Assessing normality for univariate marginal
distribution
81
3.11.2
Evaluating bivariate normality
85
3.11.3
Evaluating multivariate normality
86
3.12
Transformations Making the Data Near Normal
88
3.13
Robust Estimation of Location and Scale Parameters
91
3.14
Exercises and Complements
94
4:
Distributions Arising Out of the Multivariate
Normal Distribution
101 - 127
4.1
Introduction
101
4.2
Wishart
Distribution
101
4.2.1
Properties of the
Wishart
distribution
103
4.2.2
Distribution of X CX
108
4.2.3
Non-central
Wishart
distribution 111
4.2.4
Eigenvalues of
a
Wishart
matrix 111
4.3
Hotelling s
Г2
Distribution 111
4.3.1
Non-central Hotelling s
Г2
distribution
117
4.4
Wilks Statistic
118
Contents xiii
4.5
Some Statistics Based on Eigenvalues of
Wishart
Matrices
121
4.5.1
Equivalence of statistics when m#
= 1 124
4.6
Exercises and Complements
125
5:
Testing of Hypotheses
129 - 181
5.1
Introduction
129
5.2
Likelihood Ratio Test
130
5.3
Testing for a Single Population Mean
131
5.3.1
Union-intersection method
132
5.4
Equivalence Between Hotelling s T2 and
Likelihood Ratio Test
134
5.5
Confidence Region and Simultaneous Confidence Intervals
135
5.5.1
T2-Simultaneous confidence intervals
137
5.5.2
Bonferroni s simultaneous confidence intervals
140
5.6
Large Sample Inference About
μ
142
5.7
Comparing Mean Vectors of Two Populations
143
5.7.1
Union-intersection method
147
5.7.2
Behrens-Fisher problem
148
5.7.3
A large-sample test
149
5.7.4
Paired comparison
150
5.7.5
Testing that all components of
μ
are equal
152
5.7.6
Testing that two subvectors have equal means
155
5.8
Testing for the Variance of a Single Population
156
5.8.1
#ο(Σ
=
&Σο), Σο
is known, but
к
unknown
158
5.8.2
#0(Σΐ2
= 0) 158
5.8.3
Blockwise independence
160
5.8.4
Hypothesis of equicorrelation matrix
161
5.9
Test for Equality of Two Dispersion Matrices
162
5.10
Profile Analysis
163
5.11
Multi-Sample Hypotheses
168
5.11.1
Hypothesis
Ηα(μ
= ... —
Џк
=
μ)
(unknown),
given
Σι =
... =
Σ*
=
Σ
(unknown)
169
5.11.2
Hypothesis
#0(Σι
= ... =
Σ*)
(test of homogeneity of covariances)
173
xjv Contents
5.11.3
Hypothesis that
к
multinormal
populations are equal
175
5.11.4
Union-intersection method
176
5.12
Some Further Tests for
Η0{μι
= ... =
Џк),
Assuming Unequal Dispersion Matrices
177
5.12.1
Eaton s test
178
5.12.2
James s test
179
5.13
Exercises and Complements
179
6:
Multivariate Regression Analysis
183 - 252
6.1
Introduction
183
6.2
Maximum Likelihood Estimators
185
6.2.1
Properties of maximum likelihood estimators
189
6.3
Least Square Estimators
190
6.3.1
Geometrical interpretation of
В
193
6.3.2
Properties of the least square estimators
193
6.3.3
Ordinary and generalized least square estimator of
В
196
6.4
Forecasting an Observation
198
6.5
Likelihood Ratio Tests for Regression Parameters
201
6.5.1
The matrix X is of full rank
202
6.5.2
The matrix X not of full rank
207
6.6
Restricted Least Square Estimator of
В
209
6.6.1
SSP matrices and their distributions
212
6.6.2
A generalized linear hypothesis
213
6.7
Some Examples
214
6.8
Testing #o by Union-Intersection Principle
221
6.8.1
Simultaneous confidence intervals
222
6.9
Mean Centered Model
224
6.10
Classical Linear Regression Model
226
6.10.1
Forecasting a new observation
228
6.10.2
Tests of hypotheses regarding regression parameters
229
6.10.3
Multiple correlation coefficient
230
6.10.4
Selection of variables
233
6.11
Proportion of Variation in
Y
Explained by
the Multivariate Model
238
Contents xv
6.12
Subset Selection for the Multivariate Regression Model
239
6.12.1
Stepwise procedures
239
6.12.2
All possible subsets
241
6.13
Growth Curve Models
244
6.13.1
Examples
244
6.13.2
A general solution
249
6.14
Exercises and Complements
251
7:
Multivariate Analysis of Variance and Covariance
253 - 296
7.1
Introduction
253
7.2
Multivariate One-Way Analysis of Variance
253
7.2.1
Univariate model
253
7.2.2
Multivariate one-way fixed effects model
256
7.2.3
Comparison among
MÁNOVA
tests
262
7.2.4
Testing a contrast
263
7.3
Multivariate Two-Way Fixed Effects Model
266
7.3.1
Univariate case: One observation per cell
266
7.3.2
Multivariate two-way fixed effects model
(one observation per cell)
269
7.3.3
Univariate case:
r
observations per cell
270
7.3.4
Multivariate two-way fixed effects model
(r observations per cell)
274
7.4
Analysis of Covariance
279
7.4.1
A univariate general linear model
279
7.4.2
Univariate analysis of covariance:
Two-way model with one covariate
281
7.4.3
Multivariate analysis of covariance
285
7.5
A Conditional Hypothesis
293
7.6
Exercises and Complements
295
8:
Principal Component Analysis
297 - 329
8.1
Introduction
297
8.2
Population Principal Components
298
8.3
Principal Components of a Multivariate Normal
Distribution 306
xvj Contents
8.4
Sample Principal Components
306
8.5
Principal Components of Covariance Matrices with
Special Structures
312
8.6
Geometrical Interpretation of Sample Principal Components
316
8.7
Large Sample Properties of Sample Principal Components
318
8.7.1
Tests of hypotheses
321
8.8
Last Few Principal Components
325
8.8.1
Number of PC s to retain
327
8.9
Exercises and Complements
327
9:
Factor Analysis
331 - 361
9.1
Introduction
331
9.2
The Orthogonal Factor Model
332
9.2.1
Scale-invariance of factor model
335
9.2.2
Non-uniqueness of factor-loadings
336
9.2.3
Interpretation of factors
337
9.3
Estimation of Model-Parameters
338
9.3.1
Principal component method
339
9.3.2
Principal factor solution
343
9.3.3
The maximum likelihood solution
347
9.3.4
Other extraction procedures
347
9.3.5
Different types of rotation of factors
348
9.4
Factor Scores
351
9.4.1
Weighted least squares method
352
9.4.2
The regression method
353
9.5
Determining the Number of Factors
354
9.6
Comparison between Factor Analysis and Principal
Component Analysis
357
9.7
Exercises and Complements
357
10:
Canonical Correlation
363 - 388
10.1
Introduction
363
10.2
Canonical Variables and Canonical Correlations
364
Contents
xv¡¡
10.2.1
Correlation between canonical variables and
original variables
372
10.2.2
Relation between canonical correlation and
multiple correlation
374
10.3
The Sample Canonical Variables and the Sample
Canonical Correlations
375
10.3.1
Sample correlation between original variables
and sample canonical variables
378
10.3.2
Sample covariance in terms of canonical
coefficients and canonical correlation
380
10.3.3
Approximating sample covariances by first
r
canonical correlations
380
10.3.4
The proportion of total sample variance
explained by the canonical variables
383
10.4
Tests of Independence
384
10.5
Exercises and Complements
386
11:
Classification and Discrimination
389 - 451
11.1
Introduction
389
11.2
Classification in Two Groups with
Known Distributions and Known Parameters
390
11.2.1
Minimizing the total probability of
misclassification (TPM)
391
11.2.2
The likelihood ratio method
395
11.2.3
Minimizing the expected cost of
misclassification (ECM)
395
11.2.4
Maximizing the posterior probability
396
11.2.5
Minimax classification
397
11.3
Classification in Two Groups with
Known Distributions but Unknown Parameters
398
11.3.1
General Methods
398
11.3.2
Normal Populations
399
11.3.3
Evaluating classification functions: Error rates
402
11.3.4
Some examples 410
11.4
Fisher s Discriminating Function for Separating
Two Groups 413
Contents
11.4.1
Standardized discriminating functions
415
11.4.2
Tests of significance
417
11.4.3
Using Fisher s discriminating function for
classification
417
11.5
Logistic Classification:
g
= 2 418
11.5.1
Sampling designs
420
11.6
Classification in More than Two Groups
422
11.6.1
Minimum TPM rule
423
11.6.2
Minimum ECM rule
426
11.6.3
Logistic classification
426
11.7
Fisher s Method of Discrimination among
g
> 2
Populations
428
11.7.1
Fisher s discriminant procedure for classification
437
11.7.2
Relation between normal theory method and
Fisher s discrimination method
437
11.7.3
Tests of significance
439
11.7.4
Contribution of variables in separation of groups
442
11.8
Selection of Variables
444
11.9
Exercises and Complements
446
Appendix A: Matrix Algebra
453 - 491
Appendix B: Statistical Tables
493 - 524
Bibliography
525 - 534
Author Index
535 _ 538
Subject Index
539 . 549
|
| adam_txt |
Multivariate
Statistical Analysis
This textbook presents a classical approach to some techniques of
multivariate analysis in a simple and transparent manner. It offers
clear and concise development of the concepts; interpretation
of the output of the analysis; and criteria for selection of the
methods, taking into account the strengths and weaknesses of
each. With its roots in matrix algebra, for which a separate
chapter has been added as an appendix, the book includes both
data-oriented techniques and a reasonable coverage of classical
methods supplemented by comments about robustness and
general practical applicability. It also illustrates the methods of
numerical calculations at various stages.
This self-contained book is ¡deal as an advanced textbook for
graduate students in statistics and other disciplines like social,
biological and physical sciences. It will also be of benefit to
professional statisticians.
The author
¡s a
former Professor of the Indian Statistical Institute, India.
Contents
Preface
vii
Introduction
1-2
1:
Preliminaries
3-8
1.1
Introduction
3
1.2
Outline of Multivariate Methods
5
1.2.1
Dependence methods
6
1.2.2
Interdependence analysis
7
2:
Organization of Multivariate Data
9-41
2.1
Introduction
9
2.2
The Data Matrix
9
2.3
Summary Statistics
11
2.4
Linear Combination of Variables
18
2.5
Some Important Linear Transformations
20
2.6
Expectation and Covariance of Random Vectors
22
2.7
Expectation and Variance of Quadratic Forms of
Random Variables
25
2.8
Measures of Distance
27
2.9
Missing Observations
31
2.10
Exercises and Complements
34
2.11
Appendix
41
xjj Contents
3:
Multivariate
Normal Distributions and
Related Distributions
43 - 100
3.1
Introduction
43
3.2
Multivariate Normal Distribution
43
3.3
Transformation of Normal Data Matrix
58
3.4
Some Results on Quadratic Forms
60
3.5
Multivariate Central Limit Theorem
64
3.6
Maximum Likelihood Estimation of Parameters
68
3.6.1
Multivariate normal likelihood
69
3.6.2
Maximum likelihood estimation
70
3.7
Matrix Normal Distribution
77
3.8
The Multivariate
t
Distribution
77
3.9
The Dirichlet Distribution
78
3.10
Multivariate Skewness and Kurtosis
80
3.11
Examining the Assumption of Normality
81
3.11.1
Assessing normality for univariate marginal
distribution
81
3.11.2
Evaluating bivariate normality
85
3.11.3
Evaluating multivariate normality
86
3.12
Transformations Making the Data Near Normal
88
3.13
Robust Estimation of Location and Scale Parameters
91
3.14
Exercises and Complements
94
4:
Distributions Arising Out of the Multivariate
Normal Distribution
101 - 127
4.1
Introduction
101
4.2
Wishart
Distribution
101
4.2.1
Properties of the
Wishart
distribution
103
4.2.2
Distribution of X'CX
108
4.2.3
Non-central
Wishart
distribution 111
4.2.4
Eigenvalues of
a
Wishart
matrix 111
4.3
Hotelling's
Г2
Distribution 111
4.3.1
Non-central Hotelling's
Г2
distribution
117
4.4
Wilks' Statistic
118
Contents xiii
4.5
Some Statistics Based on Eigenvalues of
Wishart
Matrices
121
4.5.1
Equivalence of statistics when m#
= 1 124
4.6
Exercises and Complements
125
5:
Testing of Hypotheses
129 - 181
5.1
Introduction
129
5.2
Likelihood Ratio Test
130
5.3
Testing for a Single Population Mean
131
5.3.1
Union-intersection method
132
5.4
Equivalence Between Hotelling's T2 and
Likelihood Ratio Test
134
5.5
Confidence Region and Simultaneous Confidence Intervals
135
5.5.1
T2-Simultaneous confidence intervals
137
5.5.2
Bonferroni's simultaneous confidence intervals
140
5.6
Large Sample Inference About
μ
142
5.7
Comparing Mean Vectors of Two Populations
143
5.7.1
Union-intersection method
147
5.7.2
Behrens-Fisher problem
148
5.7.3
A large-sample test
149
5.7.4
Paired comparison
150
5.7.5
Testing that all components of
μ
are equal
152
5.7.6
Testing that two subvectors have equal means
155
5.8
Testing for the Variance of a Single Population
156
5.8.1
#ο(Σ
=
&Σο), Σο
is known, but
к
unknown
158
5.8.2
#0(Σΐ2
= 0) 158
5.8.3
Blockwise independence
160
5.8.4
Hypothesis of equicorrelation matrix
161
5.9
Test for Equality of Two Dispersion Matrices
162
5.10
Profile Analysis
163
5.11
Multi-Sample Hypotheses
168
5.11.1
Hypothesis
Ηα(μ\
= . —
Џк
=
μ)
(unknown),
given
Σι =
. =
Σ*
=
Σ
(unknown)
169
5.11.2
Hypothesis
#0(Σι
= . =
Σ*)
(test of homogeneity of covariances)
173
xjv Contents
5.11.3
Hypothesis that
к
multinormal
populations are equal
175
5.11.4
Union-intersection method
176
5.12
Some Further Tests for
Η0{μι
= . =
Џк),
Assuming Unequal Dispersion Matrices
177
5.12.1
Eaton's test
178
5.12.2
James's test
179
5.13
Exercises and Complements
179
6:
Multivariate Regression Analysis
183 - 252
6.1
Introduction
183
6.2
Maximum Likelihood Estimators
185
6.2.1
Properties of maximum likelihood estimators
189
6.3
Least Square Estimators
190
6.3.1
Geometrical interpretation of
В
193
6.3.2
Properties of the least square estimators
193
6.3.3
Ordinary and generalized least square estimator of
В
196
6.4
Forecasting an Observation
198
6.5
Likelihood Ratio Tests for Regression Parameters
201
6.5.1
The matrix X is of full rank
202
6.5.2
The matrix X not of full rank
207
6.6
Restricted Least Square Estimator of
В
209
6.6.1
SSP matrices and their distributions
212
6.6.2
A generalized linear hypothesis
213
6.7
Some Examples
214
6.8
Testing #o by Union-Intersection Principle
221
6.8.1
Simultaneous confidence intervals
222
6.9
Mean Centered Model
224
6.10
Classical Linear Regression Model
226
6.10.1
Forecasting a new observation
228
6.10.2
Tests of hypotheses regarding regression parameters
229
6.10.3
Multiple correlation coefficient
230
6.10.4
Selection of variables
233
6.11
Proportion of Variation in
Y
Explained by
the Multivariate Model
238
Contents xv
6.12
Subset Selection for the Multivariate Regression Model
239
6.12.1
Stepwise procedures
239
6.12.2
All possible subsets
241
6.13
Growth Curve Models
244
6.13.1
Examples
244
6.13.2
A general solution
249
6.14
Exercises and Complements
251
7:
Multivariate Analysis of Variance and Covariance
253 - 296
7.1
Introduction
253
7.2
Multivariate One-Way Analysis of Variance
253
7.2.1
Univariate model
253
7.2.2
Multivariate one-way fixed effects model
256
7.2.3
Comparison among
MÁNOVA
tests
262
7.2.4
Testing a contrast
263
7.3
Multivariate Two-Way Fixed Effects Model
266
7.3.1
Univariate case: One observation per cell
266
7.3.2
Multivariate two-way fixed effects model
(one observation per cell)
269
7.3.3
Univariate case:
r
observations per cell
270
7.3.4
Multivariate two-way fixed effects model
(r observations per cell)
274
7.4
Analysis of Covariance
279
7.4.1
A univariate general linear model
279
7.4.2
Univariate analysis of covariance:
Two-way model with one covariate
281
7.4.3
Multivariate analysis of covariance
285
7.5
A Conditional Hypothesis
293
7.6
Exercises and Complements
295
8:
Principal Component Analysis
297 - 329
8.1
Introduction
297
8.2
Population Principal Components
298
8.3
Principal Components of a Multivariate Normal
Distribution 306
xvj Contents
8.4
Sample Principal Components
306
8.5
Principal Components of Covariance Matrices with
Special Structures
312
8.6
Geometrical Interpretation of Sample Principal Components
316
8.7
Large Sample Properties of Sample Principal Components
318
8.7.1
Tests of hypotheses
321
8.8
Last Few Principal Components
325
8.8.1
Number of PC's to retain
327
8.9
Exercises and Complements
327
9:
Factor Analysis
331 - 361
9.1
Introduction
331
9.2
The Orthogonal Factor Model
332
9.2.1
Scale-invariance of factor model
335
9.2.2
Non-uniqueness of factor-loadings
336
9.2.3
Interpretation of factors
337
9.3
Estimation of Model-Parameters
338
9.3.1
Principal component method
339
9.3.2
Principal factor solution
343
9.3.3
The maximum likelihood solution
347
9.3.4
Other extraction procedures
347
9.3.5
Different types of rotation of factors
348
9.4
Factor Scores
351
9.4.1
Weighted least squares method
352
9.4.2
The regression method
353
9.5
Determining the Number of Factors
354
9.6
Comparison between Factor Analysis and Principal
Component Analysis
357
9.7
Exercises and Complements
357
10:
Canonical Correlation
363 - 388
10.1
Introduction
363
10.2
Canonical Variables and Canonical Correlations
364
Contents
xv¡¡
10.2.1
Correlation between canonical variables and
original variables
372
10.2.2
Relation between canonical correlation and
multiple correlation
374
10.3
The Sample Canonical Variables and the Sample
Canonical Correlations
375
10.3.1
Sample correlation between original variables
and sample canonical variables
378
10.3.2
Sample covariance in terms of canonical
coefficients and canonical correlation
380
10.3.3
Approximating sample covariances by first
r
canonical correlations
380
10.3.4
The proportion of total sample variance
explained by the canonical variables
383
10.4
Tests of Independence
384
10.5
Exercises and Complements
386
11:
Classification and Discrimination
389 - 451
11.1
Introduction
389
11.2
Classification in Two Groups with
Known Distributions and Known Parameters
390
11.2.1
Minimizing the total probability of
misclassification (TPM)
391
11.2.2
The likelihood ratio method
395
11.2.3
Minimizing the expected cost of
misclassification (ECM)
395
11.2.4
Maximizing the posterior probability
396
11.2.5
Minimax classification
397
11.3
Classification in Two Groups with
Known Distributions but Unknown Parameters
398
11.3.1
General Methods
398
11.3.2
Normal Populations
399
11.3.3
Evaluating classification functions: Error rates
402
11.3.4
Some examples 410
11.4
Fisher's Discriminating Function for Separating
Two Groups 413
Contents
11.4.1
Standardized discriminating functions
415
11.4.2
Tests of significance
417
11.4.3
Using Fisher's discriminating function for
classification
417
11.5
Logistic Classification:
g
= 2 418
11.5.1
Sampling designs
420
11.6
Classification in More than Two Groups
422
11.6.1
Minimum TPM rule
423
11.6.2
Minimum ECM rule
426
11.6.3
Logistic classification
426
11.7
Fisher's Method of Discrimination among
g
> 2
Populations
428
11.7.1
Fisher's discriminant procedure for classification
437
11.7.2
Relation between normal theory method and
Fisher's discrimination method
437
11.7.3
Tests of significance
439
11.7.4
Contribution of variables in separation of groups
442
11.8
Selection of Variables
444
11.9
Exercises and Complements
446
Appendix A: Matrix Algebra
453 - 491
Appendix B: Statistical Tables
493 - 524
Bibliography
525 - 534
Author Index
535 _ 538
Subject Index
539 . 549 |
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| author | Mukhopadhyay, Parimal |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| index_date | 2024-07-02T23:00:26Z |
| indexdate | 2024-07-09T21:27:01Z |
| institution | BVB |
| isbn | 9812791752 9789812791757 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016994330 |
| oclc_num | 191658559 |
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| owner_facet | DE-703 DE-91G DE-BY-TUM DE-824 |
| physical | XVIII, 549 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Mukhopadhyay, Parimal Verfasser (DE-588)170031993 aut Multivariate statistical analysis Parimal Mukhopadhyay Singapore [u.a.] World Scientific 2009 XVIII, 549 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994330&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994330&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mukhopadhyay, Parimal Multivariate statistical analysis Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4040708-1 |
| title | Multivariate statistical analysis |
| title_auth | Multivariate statistical analysis |
| title_exact_search | Multivariate statistical analysis |
| title_exact_search_txtP | Multivariate statistical analysis |
| title_full | Multivariate statistical analysis Parimal Mukhopadhyay |
| title_fullStr | Multivariate statistical analysis Parimal Mukhopadhyay |
| title_full_unstemmed | Multivariate statistical analysis Parimal Mukhopadhyay |
| title_short | Multivariate statistical analysis |
| title_sort | multivariate statistical analysis |
| topic | Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Multivariate analysis Multivariate Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994330&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994330&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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