Saddlepoint approximations with applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | Cambridge series in statistical and probabilistic mathematics
|
| Subjects: | |
| Online Access: | Publisher description Table of contents only Contributor biographical information Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 564 S. graph. Darst. 26 cm |
| ISBN: | 9780521872508 0521872502 |
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Record in the Search Index
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| adam_text | Titel: Saddlepoint approximations with applications
Autor: Butler, Ronald W.
Jahr: 2007
Contents
Preface page ix
1 Fundamental approximations 1
1.1 Univariate densities and mass functions 1
1.2 Univariate cumulative distribution functions 12
1.3 Failure (hazard) rate, approximation 28
1.4 Final remarks 30
1.5 Computational notes 30
1.6 Exercises 31
2 Properties and derivations 38
2.1 Simple properties of the approximations 38
2.2 Saddlepoint density 41
2.3 Saddlepoint CDF approximation 49
2.4 Further topics 54
2.5 Appendix 66
2.6 Exercises 70
3 Multivariate densities 75
3.1 Saddlepoint density and mass functions 75
3.2 Development of the saddlepoint density 83
3.3 Properties of multivariate saddlepoint densities 91
3.4 Further examples 93
3.5 Multivariate CDFs 101
3.6 Exercises 102
4 Conditional densities and distribution functions 107
4.1 Conditional saddlepoint density and mass functions 107
4.2 Conditional cumulative distribution functions 113
4.3 Further examples: Linear combinations of independent variables 123
4.4 Further topics 126
4.5 Appendix 132
4.6 Exercises 136
vi Contents
5 Exponential families and tilted distributions 145
5.1 Regular exponential families 145
5.2 Edgeworth expansions 151
5.3 Tilted exponential families and saddlepoint approximations 156
5.4 Saddlepoint approximation in regular exponential families 158
5.5 Exercises 179
6 Further exponential family examples and theory 183
6.1 Logistic regression and LD50 estimation 183
6.2 Common odds ratio in 2 x 2 tables 193
6.3 Times series analysis of truncated count data 208
6.4 Exponential families of Markov processes 209
6.5 Truncation 212
6.6 Exercises 213
7 Probability computation with p* 219
7.1 The p* density in regular exponential families 219
7.2 Conditional inference and p* in group transformation models 225
7.3 Approximate conditional inference and p* in curved exponential families 230
7.4 Appendix 250
7.5 Exercises 254
8 Probabilities with r*-type approximations 259
8.1 Notation, models, and sample space derivatives 259
8.2 Scalar parameter approximations 260
8.3 Examples 261
8.4 Derivation of (8.1) 265
8.5 Other versions of û 266
8.6 Numerical examples 271
8.7 Properties 278
8.8 Appendix 279
8.9 Exercises 282
9 Nuisance parameters 285
9.1 Approximation with nuisance parameters 285
9.2 Examples 286
9.3 Derivation of (9.3) and (9.4) 291
9.4 Exact and approximate sample space derivatives 292
9.5 Numerical examples 294
9.6 Variation independence, conditional likelihood, and marginal likelihood 297
9.7 Examples 304
9.8 Properties of (9.3) 314
9.9 Exercises 315
10 Sequential saddlepoint applications 323
10.1 Sequential saddlepoint approximation 323
Contents vii
10.2 Comparison to the double-saddlepoint approach 324
10.3 Examples 325
10.4 P-values for the Bartlett-Nanda-Pillai trace statistic 330
10.5 Exercises 334
11 Applications to multivariate testing 341
11.1 P -values in MANOVA 342
11.2 P-values in tests of covariance 348
11.3 Power functions for multivariate tests 355
11.4 Some multivariate saddlepoint densities 363
11.5 Appendix 365
11.6 Exercises 366
12 Ratios and roots of estimating equations 374
12.1 Ratios 375
12.2 Univariate roots of estimating equations 384
12.3 Distributions for vector ratios 392
12.4 Multivariate roots of estimating equations 401
12.5 The conditional CDF of Rm given R1..., Rm-1 411
12.6 Appendix 420
12.7 Exercises 422
13 First passage and time to event distributions 430
13.1 Semi-Markov and Markov processes with finite state space 430
13.2 Passage times with a single destination state 435
13.3 Passage times with many possible destination states 452
13.4 Birth and death processes and modular systems 454
13.5 Markov processes 461
13.6 A redundant and repairable system 462
13.7 Appendix 466
13.8 Exercises 469
14 Bootstrapping in the transform domain 474
14.1 Saddlepoint approximation to the single bootstrap distribution 475
14.2 Saddlepoint approximations for double bootstrap confidence bands 482
14.3 Semiparametric bootstrap 487
14.4 Indirect saddlepoint approximation 494
14.5 Empirical saddlepoint approximations 500
14.6 Appendix 500
14.7 Exercises 502
15 Bayesian applications 506
15.1 Bayesian prediction with intractable predictand distribution 507
15.2 Passage time examples for Markov processes 510
15.3 Passage time examples for semi-Markov processes 517
viii Contents
15.4 Conclusions, applicability, and alternative methods 522
15.5 Computational algorithms 524
15.6 Exercises 525
528
528
532
538
539
545
548
560
16 Nonnormal bases
16.1 Nonnormal-based saddlepoint expressions
16.2 Choice of base distribution
16.3 Conditional distribution approximation
16.4 Examples
16.5 Exercises
References
Index
|
| adam_txt |
Titel: Saddlepoint approximations with applications
Autor: Butler, Ronald W.
Jahr: 2007
Contents
Preface page ix
1 Fundamental approximations 1
1.1 Univariate densities and mass functions 1
1.2 Univariate cumulative distribution functions 12
1.3 Failure (hazard) rate, approximation 28
1.4 Final remarks 30
1.5 Computational notes 30
1.6 Exercises 31
2 Properties and derivations 38
2.1 Simple properties of the approximations 38
2.2 Saddlepoint density 41
2.3 Saddlepoint CDF approximation 49
2.4 Further topics 54
2.5 Appendix 66
2.6 Exercises 70
3 Multivariate densities 75
3.1 Saddlepoint density and mass functions 75
3.2 Development of the saddlepoint density 83
3.3 Properties of multivariate saddlepoint densities 91
3.4 Further examples 93
3.5 Multivariate CDFs 101
3.6 Exercises 102
4 Conditional densities and distribution functions 107
4.1 Conditional saddlepoint density and mass functions 107
4.2 Conditional cumulative distribution functions 113
4.3 Further examples: Linear combinations of independent variables 123
4.4 Further topics 126
4.5 Appendix 132
4.6 Exercises 136
vi Contents
5 Exponential families and tilted distributions 145
5.1 Regular exponential families 145
5.2 Edgeworth expansions 151
5.3 Tilted exponential families and saddlepoint approximations 156
5.4 Saddlepoint approximation in regular exponential families 158
5.5 Exercises 179
6 Further exponential family examples and theory 183
6.1 Logistic regression and LD50 estimation 183
6.2 Common odds ratio in 2 x 2 tables 193
6.3 Times series analysis of truncated count data 208
6.4 Exponential families of Markov processes 209
6.5 Truncation 212
6.6 Exercises 213
7 Probability computation with p* 219
7.1 The p* density in regular exponential families 219
7.2 Conditional inference and p* in group transformation models 225
7.3 Approximate conditional inference and p* in curved exponential families 230
7.4 Appendix 250
7.5 Exercises 254
8 Probabilities with r*-type approximations 259
8.1 Notation, models, and sample space derivatives 259
8.2 Scalar parameter approximations 260
8.3 Examples 261
8.4 Derivation of (8.1) 265
8.5 Other versions of û 266
8.6 Numerical examples 271
8.7 Properties 278
8.8 Appendix 279
8.9 Exercises 282
9 Nuisance parameters 285
9.1 Approximation with nuisance parameters 285
9.2 Examples 286
9.3 Derivation of (9.3) and (9.4) 291
9.4 Exact and approximate sample space derivatives 292
9.5 Numerical examples 294
9.6 Variation independence, conditional likelihood, and marginal likelihood 297
9.7 Examples 304
9.8 Properties of (9.3) 314
9.9 Exercises 315
10 Sequential saddlepoint applications 323
10.1 Sequential saddlepoint approximation 323
Contents vii
10.2 Comparison to the double-saddlepoint approach 324
10.3 Examples 325
10.4 P-values for the Bartlett-Nanda-Pillai trace statistic 330
10.5 Exercises 334
11 Applications to multivariate testing 341
11.1 P -values in MANOVA 342
11.2 P-values in tests of covariance 348
11.3 Power functions for multivariate tests 355
11.4 Some multivariate saddlepoint densities 363
11.5 Appendix 365
11.6 Exercises 366
12 Ratios and roots of estimating equations 374
12.1 Ratios 375
12.2 Univariate roots of estimating equations 384
12.3 Distributions for vector ratios 392
12.4 Multivariate roots of estimating equations 401
12.5 The conditional CDF of Rm given R1., Rm-1 411
12.6 Appendix 420
12.7 Exercises 422
13 First passage and time to event distributions 430
13.1 Semi-Markov and Markov processes with finite state space 430
13.2 Passage times with a single destination state 435
13.3 Passage times with many possible destination states 452
13.4 Birth and death processes and modular systems 454
13.5 Markov processes 461
13.6 A redundant and repairable system 462
13.7 Appendix 466
13.8 Exercises 469
14 Bootstrapping in the transform domain 474
14.1 Saddlepoint approximation to the single bootstrap distribution 475
14.2 Saddlepoint approximations for double bootstrap confidence bands 482
14.3 Semiparametric bootstrap 487
14.4 Indirect saddlepoint approximation 494
14.5 Empirical saddlepoint approximations 500
14.6 Appendix 500
14.7 Exercises 502
15 Bayesian applications 506
15.1 Bayesian prediction with intractable predictand distribution 507
15.2 Passage time examples for Markov processes 510
15.3 Passage time examples for semi-Markov processes 517
viii Contents
15.4 Conclusions, applicability, and alternative methods 522
15.5 Computational algorithms 524
15.6 Exercises 525
528
528
532
538
539
545
548
560
16 Nonnormal bases
16.1 Nonnormal-based saddlepoint expressions
16.2 Choice of base distribution
16.3 Conditional distribution approximation
16.4 Examples
16.5 Exercises
References
Index |
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| index_date | 2024-07-02T19:49:33Z |
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| isbn | 9780521872508 0521872502 |
| language | English |
| lccn | 2007299640 |
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| spelling | Butler, Ronald W. Verfasser (DE-588)122858360 aut Saddlepoint approximations with applications Ronald W. Butler 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XI, 564 S. graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics Includes bibliographical references and index Col, Méthode du Method of steepest descent (Numerical analysis) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Sattelpunktmethode (DE-588)7544084-2 gnd rswk-swf Sattelpunktmethode (DE-588)7544084-2 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 http://www.loc.gov/catdir/enhancements/fy0803/2007299640-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0803/2007299640-t.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0803/2007299640-b.html Contributor biographical information HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016317097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Butler, Ronald W. Saddlepoint approximations with applications Col, Méthode du Method of steepest descent (Numerical analysis) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Sattelpunktmethode (DE-588)7544084-2 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)7544084-2 |
| title | Saddlepoint approximations with applications |
| title_auth | Saddlepoint approximations with applications |
| title_exact_search | Saddlepoint approximations with applications |
| title_exact_search_txtP | Saddlepoint approximations with applications |
| title_full | Saddlepoint approximations with applications Ronald W. Butler |
| title_fullStr | Saddlepoint approximations with applications Ronald W. Butler |
| title_full_unstemmed | Saddlepoint approximations with applications Ronald W. Butler |
| title_short | Saddlepoint approximations with applications |
| title_sort | saddlepoint approximations with applications |
| topic | Col, Méthode du Method of steepest descent (Numerical analysis) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Sattelpunktmethode (DE-588)7544084-2 gnd |
| topic_facet | Col, Méthode du Method of steepest descent (Numerical analysis) Wahrscheinlichkeitsverteilung Sattelpunktmethode |
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