Mathematical statistics:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Springer
2007
|
| Ausgabe: | 2. ed., corr. printing as of 4. printing |
| Schriftenreihe: | Springer texts in statistics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016360210&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 545 - 554 |
| Umfang: | XVI, 591 S. |
| ISBN: | 9780387953823 0387953825 |
Internformat
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| 250 | |a 2. ed., corr. printing as of 4. printing | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 620 2006 A 2422(2,2007) 0104 MAT 620 2006 A 2422(2,2007) |
|---|---|
| DE-BY-TUM_katkey | 1633281 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010091951 040010091984 |
| _version_ | 1821933192677949440 |
| adam_text | JUN SHAO
MATHEMATICA
L STATISTICS
SECOND EDITION
&J
SPRINGE
R
CONTENTS
PREFAC
E T
O TH
E FIRS
T EDITIO
N VI
I
PREFAC
E T
O TH
E SECON
D EDITIO
N I
X
CHAPTE
R 1
. PROBABILIT
Y THEOR
Y 1
1.1 PROBABILIT
Y SPACES AN
D RANDO
M ELEMENT
S 1
1.1.1 CR-FIELDS AN
D MEASURE
S 1
1.1.2 MEASURABL
E FUNCTIONS AN
D DISTRIBUTION
S 6
1.2 INTEGRATIO
N AN
D DIFFERENTIATION 10
1.2.1 INTEGRATIO
N 10
1.2.2 RADON-NIKODY
M DERIVATIV
E 15
1.3 DISTRIBUTION
S AN
D THEI
R CHARACTERISTIC
S 17
1.3.1 DISTRIBUTION
S AN
D PROBABILIT
Y DENSITIE
S 17
1.3.2 MOMENT
S AN
D MOMEN
T INEQUALITIE
S 28
1.3.3 MOMEN
T GENERATIN
G AN
D CHARACTERISTI
C FUNCTIONS ..
. 32
1.4 CONDITIONA
L EXPECTATION
S 37
1.4.1 CONDITIONA
L EXPECTATION
S 37
1.4.2 INDEPENDENC
E 4
1
1.4.3 CONDITIONA
L DISTRIBUTION
S 43
1.4.4 MARKO
V CHAIN
S AN
D MARTINGALE
S 45
1.5 ASYMPTOTI
C THEOR
Y 49
1.5.1 CONVERGENCE MODE
S AN
D STOCHASTI
C ORDER
S 50
1.5.2 WEAK CONVERGENCE 56
1.5.3 CONVERGENCE OF TRANSFORMATION
S 59
1.5.4 TH
E LAW OF LARG
E NUMBER
S 62
1.5.5 TH
E CENTRA
L LIMIT THEORE
M 67
XI
XII
CONTENTS
1.5.6 EDGEWORTH AND CORNISH-FISHER EXPANSIONS 70
1.6 EXERCISES 74
CHAPTER 2. FUNDAMENTAL
S OF STATISTIC
S 9
1
2.1 POPULATIONS, SAMPLES, AND MODELS 91
2.1.1 POPULATIONS AND SAMPLES 91
2.1.2 PARAMETRIC AND NONPARAMETRIC MODELS 94
2.1.3 EXPONENTIAL AND LOCATION-SCALE FAMILIES 96
2.2 STATISTICS, SUFFICIENCY, AND COMPLETENESS 100
2.2.1 STATISTICS AND THEIR DISTRIBUTIONS 100
2.2.2 SUFFICIENCY AND MINIMAL SUFFICIENCY 103
2.2.3 COMPLETE STATISTICS 109
2.3 STATISTICAL DECISION THEORY 113
2.3.1 DECISION RULES, LOSS FUNCTIONS, AND RISKS 113
2.3.2 ADMISSIBILITY AND OPTIMALITY 116
2.4 STATISTICAL INFERENCE 122
2.4.1 POINT ESTIMATORS 122
2.4.2 HYPOTHESIS TESTS 125
2.4.3 CONFIDENCE SETS 129
2.5 ASYMPTOTIC CRITERIA AND INFERENCE 131
2.5.1 CONSISTENCY 132
2.5.2 ASYMPTOTIC BIAS, VARIANCE, AND MSE 135
2.5.3 ASYMPTOTIC INFERENCE 139
2.6 EXERCISES 142
CHAPTE
R 3
. UNBIASE
D ESTIMATIO
N 161
3.1 THE UMVUE 161
3.1.1 SUFFICIENT AND COMPLETE STATISTICS 162
3.1.2 A NECESSARY AND SUFFICIENT CONDITION 166
3.1.3 INFORMATION INEQUALITY 169
3.1.4 ASYMPTOTIC PROPERTIES OF UMVUE S 172
3.2 U-STATISTICS 174
3.2.1 SOME EXAMPLES 174
3.2.2 VARIANCES OF U-STATISTICS 176
3.2.3 THE PROJECTION METHOD 178
CONTENTS
XIII
3.3 TH
E LS
E IN LINEA
R MODELS 182
3.3.1 TH
E LSE AN
D ESTIMABILIT
Y 182
3.3.2 TH
E UMVU
E AN
D BLU
E 186
3.3.3 ROBUSTNES
S OF LSE
S 189
3.3.4 ASYMPTOTI
C PROPERTIE
S OF LSE
S 193
3.4 UNBIASE
D ESTIMATOR
S IN SURVEY PROBLEM
S 195
3.4.1 UMVUE
S OF POPULATIO
N TOTAL
S 195
3.4.2 HORVITZ-THOMPSO
N ESTIMATOR
S 199
3.5 ASYMPTOTICALL
Y UNBIASE
D ESTIMATOR
S 204
3.5.1 FUNCTION
S OF UNBIASE
D ESTIMATOR
S 204
3.5.2 TH
E METHO
D OF MOMENT
S 207
3.5.3 V-STATISTIC
S 210
3.5.4 TH
E WEIGHTED LSE 213
3.6 EXERCISES 217
CHAPTE
R 4
. ESTIMATIO
N I
N PARAMETRI
C MODEL
S 23
1
4.1 BAYES DECISIONS AN
D ESTIMATOR
S 231
4.1.1 BAYES ACTION
S 231
4.1.2 EMPIRICA
L AN
D HIERARCHICA
L BAYES METHOD
S 236
4.1.3 BAYES RULES AN
D ESTIMATOR
S 239
4.1.4 MARKO
V CHAI
N MONT
E CARL
O 245
4.2 INVARIANC
E 251
4.2.1 ONE-PARAMETE
R LOCATIO
N FAMILIES 251
4.2.2 ONE-PARAMETE
R SCALE FAMILIES 255
4.2.3 GENERA
L LOCATION-SCAL
E FAMILIES 257
4.3 MINIMAXIT
Y AN
D ADMISSIBILITY 261
4.3.1 ESTIMATOR
S WIT
H CONSTAN
T RISKS 261
4.3.2 RESULT
S IN ONE-PARAMETE
R EXPONENTIA
L FAMILIES ...
. 265
4.3.3 SIMULTANEOU
S ESTIMATIO
N AN
D SHRINKAG
E ESTIMATOR
S . . 267
4.4 TH
E METHO
D OF MAXIMU
M LIKELIHOOD 273
4.4.1 TH
E LIKELIHOOD FUNCTION AN
D MLE
S 273
4.4.2 MLE
S IN GENERALIZED LINEA
R MODEL
S 279
4.4.3 QUASI-LIKELIHOODS AN
D CONDITIONA
L LIKELIHOODS 283
4.5 ASYMPTOTICALL
Y EFFICIENT ESTIMATIO
N 286
4.5.1 ASYMPTOTI
C OPTIMALIT
Y 286
XIV
CONTENTS
4.5.2 ASYMPTOTIC EFFICIENCY OF MLE S AND RLE S 290
4.5.3 OTHER ASYMPTOTICALLY EFFICIENT ESTIMATORS 295
4.6 EXERCISES 299
CHAPTER
5.
ESTIMATIO
N
I
N
NONPARAMETRI
C
MODEL
S
319
5.1 DISTRIBUTION ESTIMATORS 319
5.1.1 EMPIRICAL C.D.F. S IN I.I.D. CASES 320
5.1.2 EMPIRICAL LIKELIHOODS 323
5.1.3 DENSITY ESTIMATION 330
5.1.4 SEMI-PARAMETRIC METHODS 333
5.2 STATISTICAL FUNCTIONA
L 338
5.2.1 DIFFERENTIABILITY AND ASYMPTOTIC NORMALITY 338
5.2.2 L-, M-, AND R-ESTIMATORS AND RANK STATISTICS 343
5.3 LINEAR FUNCTIONS OF ORDER STATISTICS 351
5.3.1 SAMPLE QUANTILES 351
5.3.2 ROBUSTNESS AND EFFICIENCY 355
5.3.3 L-ESTIMATORS IN LINEAR MODELS 358
5.4 GENERALIZED ESTIMATING EQUATIONS 359
5.4.1 THE GEE METHOD AND ITS RELATIONSHIP WITH OTHERS . . 360
5.4.2 CONSISTENCY OF GEE ESTIMATORS 363
5.4.3 ASYMPTOTIC NORMALITY OF GEE ESTIMATORS 367
5.5 VARIANCE ESTIMATION 371
5.5.1 THE SUBSTITUTION METHOD 372
5.5.2 THEJACKKNIFE 376
5.5.3 THE BOOTSTRAP 380
5.6 EXERCISES 383
CHAPTER 6. HYPOTHESI
S TEST
S 39
3
6.1 UMP TESTS 393
6.1.1 THE NEYMAN-PEARSON LEMMA 394
6.1.2 MONOTONE LIKELIHOOD RATIO 397
6.1.3 UMP TESTS FOR TWO-SIDED HYPOTHESES 401
6.2 UMP UNBIASED TESTS 404
6.2.1 UNBIASEDNESS, SIMILARITY, AND NEYMAN STRUCTURE . . . 404
6.2.2 UMPU TESTS IN EXPONENTIAL FAMILIES 406
6.2.3 UMPU TESTS IN NORMAL FAMILIES 410
CONTENTS
XV
6.3 UMP INVARIANT TESTS 417
6.3.1 INVARIANCE AND UMPI TESTS 417
6.3.2 UMPI TESTS IN NORMAL LINEAR MODELS 422
6.4 TESTS IN PARAMETRIC MODELS 428
6.4.1 LIKELIHOOD RATIO TESTS 428
6.4.2 ASYMPTOTIC TESTS BASED ON LIKELIHOODS 431
6.4.3 X
2
-TESTS 436
6.4.4 BAYES TESTS 440
6.5 TESTS IN NONPARAMETRIC MODELS 442
6.5.1 SIGN, PERMUTATION, AND RANK TESTS 442
6.5.2 KOLMOGOROV-SMIRNOV AND CRAMER-VON MISES TESTS . . 446
6.5.3 EMPIRICAL LIKELIHOOD RATIO TESTS 449
6.5.4 ASYMPTOTIC TESTS 452
6.6 EXERCISES 454
CHAPTE
R 7. CONFIDENC
E SET
S 47
1
7.1 CONSTRUCTIO
N OF CONFIDENCE SETS 471
7.1.1 PIVOTA
L QUANTITIE
S 471
7.1.2 INVERTIN
G ACCEPTANC
E REGIONS OF TEST
S 477
7.1.3 TH
E BAYESIA
N APPROAC
H 480
7.1.4 PREDICTIO
N SET
S 482
7.2 PROPERTIE
S OF CONFIDENCE SETS 484
7.2.1 LENGTH
S OF CONFIDENCE INTERVAL
S 484
7.2.2 UMA AN
D UMAU CONFIDENCE SET
S 488
7.2.3 RANDOMIZE
D CONFIDENCE SET
S 491
7.2.4 INVARIAN
T CONFIDENCE SET
S 493
7.3 ASYMPTOTI
C CONFIDENCE SETS 495
7.3.1 ASYMPTOTICALL
Y PIVOTA
L QUANTITIE
S 495
7.3.2 CONFIDENCE SET
S BASE
D O
N LIKELIHOODS 497
7.3.3 CONFIDENCE INTERVAL
S FOR QUANTILE
S 501
7.3.4 ACCURAC
Y OF ASYMPTOTI
C CONFIDENCE SET
S 503
7.4 BOOTSTRA
P CONFIDENCE SET
S 505
7.4.1 CONSTRUCTIO
N OF BOOTSTRA
P CONFIDENCE INTERVAL
S ...
. 506
7.4.2 ASYMPTOTI
C CORRECTNES
S AN
D ACCURAC
Y 509
7.4.3 HIGH-ORDE
R ACCURAT
E BOOTSTRA
P CONFIDENCE SET
S ...
. 515
XVI
CONTENTS
7.5 SIMULTANEOU
S CONFIDENCE INTERVAL
S 519
7.5.1 BONFERRONI
S METHO
D 519
7.5.2 SCHEFFE S METHO
D IN LINEAR MODEL
S 520
7.5.3 TUKEY
S METHO
D IN ONE-WAY ANOVA MODELS 523
7.5.4 CONFIDENCE BAND
S FOR C.D.F. S 525
7.6 EXERCISES 527
REFERENCES 543
LIST OF NOTATIO
N 555
LIST OF ABBREVIATION
S 557
INDEX OF DEFINITIONS, MAIN RESULTS
, AND EXAMPLE
S 559
AUTHOR INDEX 571
SUBJECT INDE
X 575
|
| any_adam_object | 1 |
| author | Shao, Jun |
| author_GND | (DE-588)170899543 |
| author_facet | Shao, Jun |
| author_role | aut |
| author_sort | Shao, Jun |
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| classification_rvk | SK 840 |
| classification_tum | MAT 620f |
| ctrlnum | (OCoLC)634873622 (DE-599)BVBBV023173568 |
| discipline | Mathematik |
| edition | 2. ed., corr. printing as of 4. printing |
| format | Book |
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| genre_facet | Aufgabensammlung |
| id | DE-604.BV023173568 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:09:51Z |
| institution | BVB |
| isbn | 9780387953823 0387953825 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016360210 |
| oclc_num | 634873622 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-91G DE-BY-TUM |
| physical | XVI, 591 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spellingShingle | Shao, Jun Mathematical statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4143389-0 |
| title | Mathematical statistics |
| title_auth | Mathematical statistics |
| title_exact_search | Mathematical statistics |
| title_full | Mathematical statistics Jun Shao |
| title_fullStr | Mathematical statistics Jun Shao |
| title_full_unstemmed | Mathematical statistics Jun Shao |
| title_short | Mathematical statistics |
| title_sort | mathematical statistics |
| topic | Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016360210&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT shaojun mathematicalstatistics |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 620 2006 A 2422(2,2007) Lageplan 0104 MAT 620 2006 A 2422(2,2007) Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 1 | Nicht ausleihbar Am Standort |