Multivariate dispersion, central regions, and depth: the lift zonoid approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
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| Schriftenreihe: | Lecture notes in statistics
165 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 291 S. graph. Darst. |
| ISBN: | 0387954120 |
Internformat
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| 245 | 1 | 0 | |a Multivariate dispersion, central regions, and depth |b the lift zonoid approach |c Karl Mosler |
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Datensatz im Suchindex
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| adam_text | KARL MOSLER MULTIVARIATE DISPERSION, CENTRAL REGIONS AND DEPTH THE LIFT
ZONOID APPROACH SPRINGER CONTENTS PREFACE V 1 INTRODUCTION 1 1.1 THE
BRIEF 1 1.2 REPRESENTING A PROBABILITY MEASURE 2 1.3 LIFT ZONOIDS 4 1.4
EXAMPLES OF LIFT ZONOIDS 9 1.5 REPRESENTING DISTRIBUTIONS BY CONVEX
COMPACTS 14 1.6 ORDERING DISTRIBUTIONS 16 1.7 CENTRAL REGIONS AND DATA
DEPTH 19 1.8 STATISTICAL INFERENCE 22 2 ZONOIDS AND LIFT ZONOIDS 25 2.1
ZONOTOPES AND ZONOIDS 27 ,2.1.1 ZONOID OF A MEASURE 27 2.1.2 EQUIVALENT
DEFINITIONS OF THE ZONOID OF A MEASURE ... 30 2.1.3 SUPPORT FUNCTION OF
A ZONOID 32 2.1.4 ZONOIDS AS EXPECTED RANDOM SEGMENTS . . . . . . . . .
34 2.1.5 VOLUME OF A ZONOID 35 2.1.6 MEASURES WITH EQUAL ZONOIDS 38 2.2
LIFT ZONOID OF A MEASURE 40 2.2.1 DEFINITION AND FIRST PROPERTIES 40
2.2.2 LIFT ZONOTOPE 43 2.2.3 UNIVARIATE CASE . 43 2.3 EMBEDDING INTO
CONVEX COMPACTS 48 2.3.1 INCLUSION OF LIFT ZONOIDS 49 2.3.2 UNIQUENESS
OF THE REPRESENTATION 50 2.3.3 LIFT ZONOID METRIC 51 2.3.4 LINEAR
TRANSFORMATIONS AND PROJECTIONS 52 2.3.5 LIFT ZONOIDS OF SPHERICAL AND
ELLIPTICAL DISTRIBUTIONS . . 55 VIII CONTENTS 2.4 CONTINUITY AND
APPROXIMATION 58 2.4.1 CONVERGENCE OF LIFT ZONOIDS 59 2.4.2 MONOTONE
APPROXIMATION OF MEASURES 65 2.4.3 VOLUME OF A LIFT ZONOID 66 2.5 LIMIT
THEOREMS 68 2.6 REPRESENTATION OF MEASURES BY A FUNCTIONAL 71 2.6.1
STATISTICAL REPRESENTATIONS 74 2.6.2 LIFT ZONOIDS AND THE EMPIRICAL
PROCESS 77 2.7 NOTES 77 CENTRAL REGIONS 79 3.1 ZONOID TRIMMED REGIONS 81
3.2 PROPERTIES 84 3.3 UNIVARIATE CENTRAL REGIONS 85 3.4 EXAMPLES OF
ZONOID TRIMMED REGIONS 88 3.5 NOTIONS OF CENTRAL REGIONS 93 3.6
CONTINUITY AND LAW OF LARGE NUMBERS 96 3.7 FURTHER PROPERTIES 97 3.8
TRIMMING OF EMPIRICAL MEASURES 100 3.9 COMPUTATION OF ZONOID TRIMMED
REGIONS 102 3.10 NOTES 103 DATA DEPTH 105 4.1 ZONOID DEPTH 108 4.2
PROPERTIES OF THE ZONOID DEPTH ILL 4.3 DIFFERENT NOTIONS OF DATA DEPTH
116 4.4 COMBINATORIAL INVARIANCE . * 123 4.5- COMPUTATION OF THE ZONOID
DEPTH 127 4.6 NOTES 130 INFERENCE BASED ON DATA DEPTH 133 (BY RAINER
DYCKERHOFF ) 5.1 GENERAL NOTION OF DATA DEPTH 134 5.2 TWO-SAMPLE DEPTH
TEST FOR SCALE 136 5.3 TWO-SAMPLE RANK TEST FOR LOCATION AND SCALE 139
5.4 CLASSICAL TWO-SAMPLE TESTS . . . 141 5.4.1 BOX S M TEST 141 5.4.2
FRIEDMAN-RAFSKY TEST 142 5.4.3 HOTELLING S T 2 TEST 144 5.4.4 PURI-SEN
TEST 145 5.5 A NEW WILCOXON DISTANCE TEST 147 5.6 POWER COMPARISON 149
CONTENTS IX 5.7 NOTES 163 DEPTH OF HYPERPLANES 165 6.1 DEPTH OF A
HYPERPLANE AND MHD OF A SAMPLE 166 6.2 PROPERTIES OF MHD AND MAJORITY
DEPTH 168 6.3 COMBINATORIAL INVARIANCE 171 6.4 MEASURING COMBINATORIAL
DISPERSION 173 6.5 MHD STATISTICS 174 6.6 SIGNIFICANCE TESTS AND THEIR
POWER 174 6.7 NOTES 179 VOLUME STATISTICS 181 7.1 UNIVARIATE GINI INDEX
182 7.2 LIFT ZONOID VOLUME 186 7.3 EXPECTED VOLUME OF A RANDOM CONVEX
HULL 188 7.4 THE MULTIVARIATE VOLUME-GINI INDEX 191 7.5 VOLUME
STATISTICS IN CLUSTER ANALYSIS 197 7.6 MEASURING DEPENDENCY 198 7.7
NOTES 205 ORDERINGS AND INDICES OF DISPERSION 207 8.1 LIFT ZONOID ORDER
208 8.2 ORDER OF MARGINALS AND INDEPENDENCE 213 8.3 ORDER OF
CONVOLUTIONS 214 8.4 LIFT ZONOID ORDER VS. CONVEX ORDER 216 8.5 VOLUME
INEQUALITIES AND RANDOM DETERMINANTS 219 8.6 INCREASING, SCALED, AND
CENTERED ORDERS . .... 219 8.7 * PROPERTIES OF DISPERSION ORDERS 222 8.8
MULTIVARIATE INDICES OF DISPERSION 224 8.9 NOTES 228 ECONOMIC DISPARITY
AND CONCENTRATION 229 9.1 MEASURING ECONOMIC INEQUALITY 230 9.2 INVERSE
LORENZ FUNCTION (ILF) 232 9.3 PRICE LORENZ ORDER 238 9.4 MAJORIZATIONS
OF ABSOLUTE ENDOWMENTS 242 9.5 OTHER INEQUALITY ORDERINGS 245 9.6
MEASURING INDUSTRIAL CONCENTRATION 248 9.7 MULTIVARIATE CONCENTRATION
FUNCTION 252 9.8 MULTIVARIATE CONCENTRATION INDICES 255 9.9 NOTES 257
APPENDIX A: BASIC NOTIONS 259
|
| any_adam_object | 1 |
| author | Mosler, Karl C. 1947- |
| author_GND | (DE-588)118195042 |
| author_facet | Mosler, Karl C. 1947- |
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| building | Verbundindex |
| bvnumber | BV014497354 |
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| callnumber-label | QA273 |
| callnumber-raw | QA273.6.M68 2002 |
| callnumber-search | QA273.6.M68 2002 |
| callnumber-sort | QA 3273.6 M68 42002 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 856 SK 800 |
| ctrlnum | (OCoLC)49705017 (DE-599)BVBBV014497354 |
| dewey-full | 519.221 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 21 519.2 |
| dewey-search | 519.2 21 519.2 |
| dewey-sort | 3519.2 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T19:03:07Z |
| institution | BVB |
| isbn | 0387954120 |
| language | English |
| lccn | 2002067536 |
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| physical | X, 291 S. graph. Darst. |
| publishDate | 2002 |
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| publisher | Springer |
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| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Mosler, Karl C. 1947- Verfasser (DE-588)118195042 aut Multivariate dispersion, central regions, and depth the lift zonoid approach Karl Mosler New York [u.a.] Springer 2002 X, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 165 Mesures de probabilités Probability measures Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Wahrscheinlichkeitsmaß (DE-588)4137556-7 s DE-604 Lecture notes in statistics 165 (DE-604)BV002447846 165 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009883244&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mosler, Karl C. 1947- Multivariate dispersion, central regions, and depth the lift zonoid approach Lecture notes in statistics Mesures de probabilités Probability measures Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4137556-7 (DE-588)4040708-1 |
| title | Multivariate dispersion, central regions, and depth the lift zonoid approach |
| title_auth | Multivariate dispersion, central regions, and depth the lift zonoid approach |
| title_exact_search | Multivariate dispersion, central regions, and depth the lift zonoid approach |
| title_full | Multivariate dispersion, central regions, and depth the lift zonoid approach Karl Mosler |
| title_fullStr | Multivariate dispersion, central regions, and depth the lift zonoid approach Karl Mosler |
| title_full_unstemmed | Multivariate dispersion, central regions, and depth the lift zonoid approach Karl Mosler |
| title_short | Multivariate dispersion, central regions, and depth |
| title_sort | multivariate dispersion central regions and depth the lift zonoid approach |
| title_sub | the lift zonoid approach |
| topic | Mesures de probabilités Probability measures Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Mesures de probabilités Probability measures Wahrscheinlichkeitsmaß Multivariate Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009883244&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT moslerkarlc multivariatedispersioncentralregionsanddepththeliftzonoidapproach |