The statistical analysis of compositional data:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Chapman and Hall
1986
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Monographs on statistics and applied probability
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 416 S. graph. Darst. |
| ISBN: | 0412280604 |
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Datensatz im Suchindex
| _version_ | 1804118012480978944 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE 1 COMPOSITIONAL DATA: SOME CHALLENGING PROBLEMS .1 INTRODUCTION
.2 GEOCHEMICAL COMPOSITIONS OF ROCKS
.3 SEDIMENTS AT DIFFERENT DEPTHS .4 TERNARY DIAGRAMS .5 PARTIAL ANALYSES
AND SUBCOMPOSITIONS .6 SUPERVISORY BEHAVIOUR
.7 HOUSEHOLD BUDGET SURVEYS 1.8 STEROID METABOLITE PATTERNS IN ADULTS
AND CHILDREN
.9 ACTIVITY PATTERNS OF A STATISTICIAN .10 CALIBRATION OF WHITE-CELL
COMPOSITIONS .11 FRUIT EVALUATION .12 FIREWORK MIXTURES .13 CLAM ECOLOGY
1.14 BIBLIOGRAPHIC NOTES PROBLEMS
2 THE SIMPLEX AS SAMPLE SPACE 2.1 CHOICE OF SAMPLE SPACE 2.2
COMPOSITIONS AND SIMPLEXES 2.3 SPACES, VECTORS, MATRICES 2.4 BASES AND
COMPOSITIONS 2.5 SUBCOMPOSITIONS
2.6 AMALGAMATIONS 2.7 PARTITIONS -2.8 PERTURBATIONS
PAGE XIII
1 1 2
4 5 8
12 13
14 15 16 17 17 18 19 20
24 24 25 28
30 33 36 38 42
IMAGE 2
2.9 GEOMETRICAL REPRESENTATIONS OF COMPOSITIONAL
DATA 43
2.10 BIBLIOGRAPHIC NOTES 44
PROBLEMS 45
THE SPECIAL DIFFICULTIES OF COMPOSITIONAL DATA ANALYSIS 48 3.1
INTRODUCTION 48
3.2 HIGH DIMENSIONALITY 50
3.3 ABSENCE OF AN INTERPRETABLE COVARIANCE STRUCTURE 52 3.4 DIFFICULTY
OF PARAMETRIC MODELLING 58
3.5 THE MIXTURE VARIATION DIFFICULTY 61
3.6 BIBLIOGRAPHIC NOTES 61
PROBLEMS 62
COVARIANCE STRUCTURE 64
4.1 FUNDAMENTALS 64
4.2 SPECIFICATION OF THE COVARIANCE STRUCTURE 66
4.3 THE COMPOSITIONAL VARIATION ARRAY 68
4.4 RECOVERY OF THE COMPOSITIONAL VARIATION ARRAY FROM THE CRUDE MEAN
VECTOR AND COVARIANCE MATRIX 71
4.5 SUBCOMPOSITIONAL ANALYSIS 73
4.6 MATRIX SPECIFICATIONS OF COVARIANCE STRUCTURES 75 4.7 SOME IMPORTANT
ELEMENTARY MATRICES 81
4.8 RELATIONSHIPS BETWEEN THE MATRIX SPECIFICATIONS 82 4.9 ESTIMATED
MATRICES FOR HONGITE COMPOSITIONS 83 4.10 LOGRATIOS AND LOGCONTRASTS 83
4.11 COVARIANCE STRUCTURE OF A BASIS 86
4.12 COMMENTARY 87
4.13 BIBLIOGRAPHIC NOTES 88
PROBLEMS 89
PROPERTIES OF MATRIX COVARIANCE SPECIFICATIONS 92 5.1 LOGRATIO NOTATION
92
5.2 LOGCONTRAST VARIANCES AND COVARIANCES 93
5.3 PERMUTATIONS 93
5.4 PROPERTIES OF P AND Q P MATRICES 95
5.5 PERMUTATION INVARIANTS INVOLVING E 95
5.6 COVARIANCE MATRIX INVERSES 98
5.7 SUBCOMPOSITIONS 100
5.8 EQUIVALENCE OF CHARACTERISTICS OF T,L,F 101
IMAGE 3
CONTENTS IX
5.9 LOGRATIO-UNCORRELATED COMPOSITIONS 105
5.10 ISOTROPIC COVARIANCE STRUCTURES 107
5.11 BIBLIOGRAPHIC NOTES 110
PROBLEMS 110
6 LOGISTIC NORMAL DISTRIBUTIONS ON THE SIMPLEX 112
6.1 INTRODUCTION 112
6.2 THE ADDITIVE LOGISTIC NORMAL CLASS 113
6.3 DENSITY FUNCTION 115
6.4 MOMENT PROPERTIES 116
6.5 COMPOSITION OF A LOGNORMAL BASIS 117
6.6 CLASS-PRESERVING PROPERTIES 118
6.7 CONDITIONAL SUBCOMPOSITIONAL PROPERTIES 122 6.8 PERTURBATION
PROPERTIES 123
6.9 A CENTRAL LIMIT THEOREM 124
6.10 A CHARACTERIZATION BY LOGCONTRASTS 125
6.11 RELATIONSHIPS WITH THE DIRICHLET CLASS 126
6.12 POTENTIAL FOR STATISTICAL ANALYSIS 129
6.13 THE MULTIPLICATIVE LOGISTIC NORMAL CLASS 130
6.14 PARTITIONED LOGISTIC NORMAL CLASSES 132
6.15 SOME NOTATION 135
6.16 BIBLIOGRAPHIC NOTES 136
PROBLEMS 137
7 LOGRATIO ANALYSIS OF COMPOSITIONS 141
7.1 INTRODUCTION 141
7.2 ESTIMATION OF FT AND E 143
7.3 VALIDATION: TESTS OF LOGISTIC NORMALITY 143
7.4 HYPOTHESIS TESTING STRATEGY AND TECHNIQUES 148 7.5 TESTING
HYPOTHESES ABOUT FT AND E 153
7.6 LOGRATIO LINEAR MODELLING 158
7.7 TESTING LOGRATIO LINEAR HYPOTHESES 162
7.8 FURTHER ASPECTS OF LOGRATIO LINEAR MODELLING 166 7.9 AN APPLICATION
OF LOGRATIO LINEAR MODELLING 170 7.10 PREDICTIVE DISTRIBUTIONS,
ATYPICALITY INDICES AND OUTLIERS 173
7.11 STATISTICAL DISCRIMINATION 176
7.12 CONDITIONAL COMPOSITIONAL MODELLING 181
7.13 BIBLIOGRAPHIC NOTES 181
PROBLEMS 182
IMAGE 4
8 DIMENSION-REDUCING TECHNIQUES 184
8.1 INTRODUCTION 184
8.2 CRUDE PRINCIPAL COMPONENT ANALYSIS 186
8.3 LOGCONTRAST PRINCIPAL COMPONENT ANALYSIS 189 8.4 APPLICATIONS OF
LOGCONTRAST PRINCIPAL COMPONENT ANALYSIS 194
8.5 SUBCOMPOSITIONAL ANALYSIS 196
8.6 APPLICATIONS OF SUBCOMPOSITIONAL ANALYSIS 198 8.7 CANONICAL
COMPONENT ANALYSIS 202
8.8 BIBLIOGRAPHIC NOTES 206
PROBLEMS 206
9 BASES AND COMPOSITIONS 208
9.1 FUNDAMENTALS 208
9.2 COVARIANCE RELATIONSHIPS 209
9.3 PRINCIPAL AND CANONICAL COMPONENT COMPARISONS 214 9.4 DISTRIBUTIONAL
RELATIONSHIPS 219
9.5 COMPOSITIONAL INVARIANCE 220
9.6 AN APPLICATION TO HOUSEHOLD BUDGET ANALYSIS 223 9.7 AN APPLICATION
TO CLINICAL BIOCHEMISTRY 226
9.8 REAPPRAISAL OF AN EARLY SHAPE AND SIZE ANALYSIS 227 9.9
BIBLIOGRAPHIC NOTES 231
PROBLEMS 232
10 SUBCOMPOSITIONS AND PARTITIONS 234
10.1 INTRODUCTION 234
10.2 COMPLETE SUBCOMPOSITIONAL INDEPENDENCE 234 10.3 PARTITIONS OF ORDER
1 241
10.4 ORDERED SEQUENCES OF PARTITIONS 247
10.5 CAVEAT 252
10.6 PARTITIONS OF HIGHER ORDER 253
10.7 BIBLIOGRAPHIC NOTES 254
PROBLEMS 254
11 IRREGULAR COMPOSITIONAL DATA 256
11.1 INTRODUCTION 256
11.2 MODELLING IMPRECISION IN COMPOSITIONS 257
11.3 ANALYSIS OF SOURCES OF IMPRECISION 261
11.4 IMPRECISION AND TESTS OF INDEPENDENCE 264
11.5 ROUNDED OR TRACE ZEROS 266
IMAGE 5
11.6 ESSENTIAL ZEROS 271
11.7 MISSING COMPONENTS 274
11.8 BIBLIOGRAPHIC NOTES 277
PROBLEMS 277
12 COMPOSITIONS IN A COVARIATE ROLE 281
12.1 INTRODUCTION 281
12.2 CALIBRATION 282
12.3 A BEFORE-AND-AFTER TREATMENT PROBLEM 283
12.4 EXPERIMENTS WITH MIXTURES 285
12.5 AN APPLICATION TO FIREWORK MIXTURES 291
12.6 CLASSIFICATION FROM COMPOSITIONS 293
12.7 AN APPLICATION TO GEOLOGICAL CLASSIFICATION 297 12.8 BIBLIOGRAPHIC
NOTES 302
PROBLEMS 302
13 FURTHER DISTRIBUTIONS ON THE SIMPLEX 305
13.1 SOME GENERALIZATIONS OF THE DIRICHLET CLASS 305 13.2 SOME
GENERALIZATIONS OF THE LOGISTIC NORMAL CLASSES 307
13.3 RECAPITULATION 309
13.4 THE S* D (A,B) CLASS 310
13.5 MAXIMUM LIKELIHOOD ESTIMATION 313
13.6 NEUTRALITY AND PARTITION INDEPENDENCE 316
13.7 SUBCOMPOSITIONAL INDEPENDENCE 318
13.8 A GENERALIZED LOGNORMAL GAMMA DISTRIBUTION WITH COMPOSITIONAL IN
VARIANCE 319
13.9 DISCUSSION 321
13.10 BIBLIOGRAPHIC NOTES 323
PROBLEMS 323
14 MISCELLANEOUS PROBLEMS 324
14.1 INTRODUCTION 324
14.2 MULTI-WAY COMPOSITIONS 324
14.3 MULTI-STAGE COMPOSITIONS 327
14.4 MULTIPLE COMPOSITIONS 329
14.5 KERNEL DENSITY ESTIMATION FOR COMPOSITIONAL DATA 332 14.6
COMPOSITIONAL STOCHASTIC PROCESSES 335
14.7 RELATION TO BAYESIAN STATISTICAL ANALYSIS 337
IMAGE 6
14.8 COMPOSITIONAL AND DIRECTIONAL DATA 338
PROBLEMS 341
APPENDICES A ALGEBRAIC PROPERTIES OF ELEMENTARY MATRICES 342
B BIBLIOGRAPHY 344
C COMPUTER SOFTWARE FOR COMPOSITIONAL DATA ANALYSIS 353 D DATA SETS 354
AUTHOR INDEX 406
SUBJECT INDEX 409
|
| any_adam_object | 1 |
| author | Aitchison, John 1926- |
| author_GND | (DE-588)141532165 |
| author_facet | Aitchison, John 1926- |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV003665354 |
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| callnumber-search | QA278 |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften Geographie |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T16:03:32Z |
| institution | BVB |
| isbn | 0412280604 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002333918 |
| oclc_num | 13215689 |
| open_access_boolean | |
| owner | DE-384 DE-473 DE-BY-UBG DE-703 DE-945 DE-29T DE-20 |
| owner_facet | DE-384 DE-473 DE-BY-UBG DE-703 DE-945 DE-29T DE-20 |
| physical | XV, 416 S. graph. Darst. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Chapman and Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Aitchison, John 1926- Verfasser (DE-588)141532165 aut The statistical analysis of compositional data J. Aitchison 1. publ. London u.a. Chapman and Hall 1986 XV, 416 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 25 Analise De Dados larpcal Analyse en composantes principales Analyse multivariée Analyse multivariée ram Corrélation (Statistique) Corrélation (statistique) ram Multivariate analyse gtt Correlation (Statistics) Multivariate analysis Korrelation (DE-588)4165343-9 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Simplex (DE-588)4181484-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Simplex <Topologie> gnd rswk-swf Simplex (DE-588)4181484-8 s Statistik (DE-588)4056995-0 s DE-604 Simplex <Topologie> f Statistische Analyse (DE-588)4116599-8 s 1\p DE-604 Multivariate Analyse (DE-588)4040708-1 s 2\p DE-604 Korrelation (DE-588)4165343-9 s 3\p DE-604 Monographs on statistics and applied probability 25 (DE-604)BV002494005 25 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002333918&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aitchison, John 1926- The statistical analysis of compositional data Monographs on statistics and applied probability Analise De Dados larpcal Analyse en composantes principales Analyse multivariée Analyse multivariée ram Corrélation (Statistique) Corrélation (statistique) ram Multivariate analyse gtt Correlation (Statistics) Multivariate analysis Korrelation (DE-588)4165343-9 gnd Multivariate Analyse (DE-588)4040708-1 gnd Simplex (DE-588)4181484-8 gnd Statistik (DE-588)4056995-0 gnd Statistische Analyse (DE-588)4116599-8 gnd |
| subject_GND | (DE-588)4165343-9 (DE-588)4040708-1 (DE-588)4181484-8 (DE-588)4056995-0 (DE-588)4116599-8 |
| title | The statistical analysis of compositional data |
| title_auth | The statistical analysis of compositional data |
| title_exact_search | The statistical analysis of compositional data |
| title_full | The statistical analysis of compositional data J. Aitchison |
| title_fullStr | The statistical analysis of compositional data J. Aitchison |
| title_full_unstemmed | The statistical analysis of compositional data J. Aitchison |
| title_short | The statistical analysis of compositional data |
| title_sort | the statistical analysis of compositional data |
| topic | Analise De Dados larpcal Analyse en composantes principales Analyse multivariée Analyse multivariée ram Corrélation (Statistique) Corrélation (statistique) ram Multivariate analyse gtt Correlation (Statistics) Multivariate analysis Korrelation (DE-588)4165343-9 gnd Multivariate Analyse (DE-588)4040708-1 gnd Simplex (DE-588)4181484-8 gnd Statistik (DE-588)4056995-0 gnd Statistische Analyse (DE-588)4116599-8 gnd |
| topic_facet | Analise De Dados Analyse en composantes principales Analyse multivariée Corrélation (Statistique) Corrélation (statistique) Multivariate analyse Correlation (Statistics) Multivariate analysis Korrelation Multivariate Analyse Simplex Statistik Statistische Analyse Simplex <Topologie> |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002333918&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT aitchisonjohn thestatisticalanalysisofcompositionaldata |