Elements of continuous multivariate analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1969
|
| Series: | Addison-Wesley series in behavioral sciences: Quantitative methods
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 388 S. graph. Darst. |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV001933891 | ||
| 003 | DE-604 | ||
| 005 | 20181004 | ||
| 007 | t | ||
| 008 | 890928s1969 d||| |||| 00||| eng d | ||
| 035 | |a (OCoLC)2873 | ||
| 035 | |a (DE-599)BVBBV001933891 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91 |a DE-384 |a DE-739 |a DE-355 |a DE-29 |a DE-29T |a DE-945 |a DE-19 |a DE-N2 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA278 | |
| 082 | 0 | |a 519 |2 18 | |
| 084 | |a QH 234 |0 (DE-625)141549: |2 rvk | ||
| 084 | |a SK 830 |0 (DE-625)143259: |2 rvk | ||
| 084 | |a 62Hxx |2 msc | ||
| 100 | 1 | |a Dempster, Arthur P. |d 1929- |e Verfasser |0 (DE-588)170358437 |4 aut | |
| 245 | 1 | 0 | |a Elements of continuous multivariate analysis |c A. P. Dempster |
| 246 | 1 | 3 | |a Continuous multivariate analysis |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1969 | |
| 300 | |a XII, 388 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley series in behavioral sciences: Quantitative methods | |
| 650 | 4 | |a Analyse multivariée | |
| 650 | 4 | |a Espaces vectoriels | |
| 650 | 4 | |a Échantillonnage (Statistique) | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Sampling (Statistics) | |
| 650 | 4 | |a Vector spaces | |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Statistik |0 (DE-588)4056995-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001260514 | ||
Record in the Search Index
| _version_ | 1804116373747531776 |
|---|---|
| adam_text | CONTENTS
PART 1 ORIENTATION
Chapter 1 Introduction
1.1 What the book is about 3
1.2 Individuals, variables, quantities, and related concepts .... 4
1.3 The role of vector space theory 6
1.4 The role of sampling theory 9
1.5 Related works: a very brief sketch 11
PART 2 MATHEMATICAL FOUNDATIONS
Chapter 2 Basic Theory of Vector Spaces
2.1 Abstract vector spaces defined 15
2.2 Subspaces, hyperplanes, linear dependence, basis vectors, and
dimension 18
2.3 Linear transformations 19
2.4 Affine geometry: vector space as geometric space 21
2.5 Matrices and coordinate systems: analytic vector space theory . . 25
2.6 Pseudoinversion 28
2.7 Exercises 30
Chapter 3 Euclidean Vector Spaces
3.1 Abstract Euclidean vector spaces 34
3.2 Euclidean geometric space 36
3.3 Orthogonal linear transformations and orthogonal projections . . 39
3.4 Positive definite symmetric matrices and orthogonal matrices . . 41
3.5 Determinants and volumes 42
3.6 Semi definite inner products 44
3.7 Exercises 47
Chapter 4 Successive Orthogonalization and Related Theory
4.1 The process of successive orthogonalization 51
4.2 Some matrix theory related to successive orthogonalizatior. ... 54
ix
X CONTENTS
4.3 Computational methods related to successive orthogonalization . 59
4.3.1 Elimination procedures 59
4.3.2 The sweep operator 62
4.3.3 The assimilation operator 67
4.3.4 The multistandardize operator 70
4.4 Situations with less than full rank 74
4.5 Exercises 76
Chapter 5 The Relation Between Two Inner Products
5.1 Basic theory 82
5.2 Relations between two ellipsoids 86
5.3 Related matrix theory 87
5.4 Computational methods 89
5.4.1 A brief description of some basic approaches 89
5.4.2 The SDG operator 95
5.5 An analytic definition of eigenvalues and eigenvectors .... 96
5.6 An application to angles between subspaces of a Euclidean space . 98
5.7 Exercises 100
Chapter 6 Dual Spaces
6.1 Basic definitions and theory 104
6.2 Dual geometric spaces 109
6.3 Some related matrix theory Ill
6.4 Duality aspects of the process of successive orthogonalization . . 112
6.5 Duality relations concerning a pair of inner products .... 113
6.6 The dual of a semi definite inner product 116
6.7 Exercises 118
PART 3 DATA ANALYSIS
Chapter 7 One Sample of Individuals: Basic Theory
7.1 Introduction 123
7.2 Definitions 124
7.3 Representation of a sample with individuals as points . . . . 126
7.4 Representation of a sample with variables as points 129
7.5 Computation oriented theory 132
7.6 Principal component analysis 136
7.7 Semi definite samples 140
7.8 Exercises 142
Chapter 8 One Sample of Individuals: Multiple Regression and Correlation
Analysis
8.1 Introduction 144
8.2 Basic description 147
8.3 Regression coefficients, correlation coefficients, and the multiple
regression analysis of VP on a subset of Vx, K2,..., KJ)_1 . . . 156
8.4 A least squares example illustrating the deletion of individuals . . 166
8.5 Correlation with a single categorical variable 170
CONTENTS xi
Chapter 9 One Sample of Individuals: Extensions of Multiple Regression
Analysis
9.1 Joint prediction of a set of variables 176
9.2 Canonical correlation analysis 177
9.3 An example illustrating exploratory use of canonical correlation
analysis 181
9.4 The case of a single classification variable represented by K,+1,
K+2, ¦•• Vv .186
9.5 The forward method of selecting predictor variables . . . . 191
9.6 An example illustrating prediction of a categorical variable and
forward selection of predictor variables 193
Chapter 10 Two or More Samples of Individuals
10.1 Introduction 201
10.2 Two sample analysis 203
10.3 Examples of two sample analysis 210
10.4 Analysis of more than two samples 219
10.5 An example with six samples cross classified into two sexes and
three races 222
10.6 Small samples on many variables 241
Chapter 11 Randomized Experimentation, Missing Values, and Covariates
11.1 General discussion 247
11.2 Examples 251
11.3 Missing values: a simple case 260
PART 4 NORMAL SAMPLING THEORY AND STATISTICAL
INFERENCE
Chapter 12 The Family of Normal Distributions
12.1 Introduction 267
12.2 Spherically distributed random outcomes 269
12.3 The normal distribution with given mean and covariance . . . 273
12.4 Basic properties of the N( l, 2) distribution 276
12.5 Standard distribution theory 278
12.6 Exercises 283
Chapter 13 Elements of Multivariate Normal Sampling Theory
13.1 Introduction 288
13.2 Sampling an origin centered normal population 288
13.3 The decomposition into random configuration and random
orientation 291
13.4 Properties and characterizations of Wishart distributions . . . 295
13.5 Properties and characterizations of the spherical distribution of a set
of orthonormal random outcomes 303
Xii CONTENTS
13.6 Multivariate t distributions and related quantities 305
13.7 Distributions and theory related to generalized beta and G
distributions 308
13.8 Remarks on probability density functions 316
13.9 Exercises 317
Chapter 14 Some Sampling Distributions and Illustrations of Postdictive
Inferences
14.1 The sample mean and sample covariance of a single sample . . 323
14.2 Sampling distributions and postdictive inference procedures for
regression and correlation analysis 332
14.3 Sampling distributions and postdictive inference procedures in the
analysis of two or more samples 346
14.4 Exercises 355
Chapter 15 The Role of Contemporary Theories of Statistical Inference
15.1 Likelihood 358
15.2 Justifications based on sampling distributions 364
15.3 Predictive inference 367
15.4 Exercises 371
Bibliography 375
Index 383
|
| any_adam_object | 1 |
| author | Dempster, Arthur P. 1929- |
| author_GND | (DE-588)170358437 |
| author_facet | Dempster, Arthur P. 1929- |
| author_role | aut |
| author_sort | Dempster, Arthur P. 1929- |
| author_variant | a p d ap apd |
| building | Verbundindex |
| bvnumber | BV001933891 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278 |
| callnumber-search | QA278 |
| callnumber-sort | QA 3278 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 234 SK 830 |
| ctrlnum | (OCoLC)2873 (DE-599)BVBBV001933891 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01684nam a2200445 c 4500</leader><controlfield tag="001">BV001933891</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20181004 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1969 d||| |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)2873</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV001933891</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-945</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-N2</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA278</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519</subfield><subfield code="2">18</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 234</subfield><subfield code="0">(DE-625)141549:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 830</subfield><subfield code="0">(DE-625)143259:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">62Hxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dempster, Arthur P.</subfield><subfield code="d">1929-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)170358437</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elements of continuous multivariate analysis</subfield><subfield code="c">A. P. Dempster</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Continuous multivariate analysis</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Reading, Mass. [u.a.]</subfield><subfield code="b">Addison-Wesley</subfield><subfield code="c">1969</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 388 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Addison-Wesley series in behavioral sciences: Quantitative methods</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse multivariée</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Espaces vectoriels</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Échantillonnage (Statistique)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multivariate analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sampling (Statistics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Vector spaces</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Statistik</subfield><subfield code="0">(DE-588)4056995-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Statistik</subfield><subfield code="0">(DE-588)4056995-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001260514</subfield></datafield></record></collection> |
| id | DE-604.BV001933891 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:29Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001260514 |
| oclc_num | 2873 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-29 DE-29T DE-945 DE-19 DE-BY-UBM DE-N2 DE-83 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-29 DE-29T DE-945 DE-19 DE-BY-UBM DE-N2 DE-83 DE-188 |
| physical | XII, 388 S. graph. Darst. |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley series in behavioral sciences: Quantitative methods |
| spelling | Dempster, Arthur P. 1929- Verfasser (DE-588)170358437 aut Elements of continuous multivariate analysis A. P. Dempster Continuous multivariate analysis Reading, Mass. [u.a.] Addison-Wesley 1969 XII, 388 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in behavioral sciences: Quantitative methods Analyse multivariée Espaces vectoriels Échantillonnage (Statistique) Multivariate analysis Sampling (Statistics) Vector spaces Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dempster, Arthur P. 1929- Elements of continuous multivariate analysis Analyse multivariée Espaces vectoriels Échantillonnage (Statistique) Multivariate analysis Sampling (Statistics) Vector spaces Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Elements of continuous multivariate analysis |
| title_alt | Continuous multivariate analysis |
| title_auth | Elements of continuous multivariate analysis |
| title_exact_search | Elements of continuous multivariate analysis |
| title_full | Elements of continuous multivariate analysis A. P. Dempster |
| title_fullStr | Elements of continuous multivariate analysis A. P. Dempster |
| title_full_unstemmed | Elements of continuous multivariate analysis A. P. Dempster |
| title_short | Elements of continuous multivariate analysis |
| title_sort | elements of continuous multivariate analysis |
| topic | Analyse multivariée Espaces vectoriels Échantillonnage (Statistique) Multivariate analysis Sampling (Statistics) Vector spaces Statistik (DE-588)4056995-0 gnd |
| topic_facet | Analyse multivariée Espaces vectoriels Échantillonnage (Statistique) Multivariate analysis Sampling (Statistics) Vector spaces Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dempsterarthurp elementsofcontinuousmultivariateanalysis AT dempsterarthurp continuousmultivariateanalysis |