In all likelihood: statistical modelling and inference using likelihood
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2007
|
| Edition: | 1. publ., [Nachdr.] |
| Series: | Oxford science publication
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 528 S. graph. Darst. |
| ISBN: | 9780198507659 0198507658 |
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MARC
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| 020 | |a 9780198507659 |9 978-0-19-850765-9 | ||
| 020 | |a 0198507658 |9 0-19-850765-8 | ||
| 035 | |a (OCoLC)255695874 | ||
| 035 | |a (DE-599)BVBBV023273710 | ||
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| 084 | |a SK 840 |0 (DE-625)143261: |2 rvk | ||
| 100 | 1 | |a Pawitan, Yudi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a In all likelihood |b statistical modelling and inference using likelihood |c Yudi Pawitan |
| 250 | |a 1. publ., [Nachdr.] | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2007 | |
| 300 | |a XIII, 528 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford science publication | |
| 650 | 4 | |a Likelihood-Funktion | |
| 650 | 4 | |a Maximum-Likelihood-Schätzung | |
| 650 | 4 | |a Wahrscheinlichkeitsrechnung - Statistisches Modell | |
| 650 | 0 | 7 | |a Likelihood-Funktion |0 (DE-588)4657256-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Likelihood-Funktion |0 (DE-588)4657256-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016458663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016458663 | ||
Record in the Search Index
| _version_ | 1804137588930379776 |
|---|---|
| adam_text | Contents
1
Introduction
1
1.1
Prototype
of statistical problems
............... 1
1.2
Statistical problems and their models
............. 3
1.3
Statistical uncertainty: inevitable controversies
....... 6
1.4
The emergence of statistics
.................. 8
1.5
Fisher and the third way
.................... 14
1.6
Exercises
............................ 19
2
Elements of likelihood inference
21
2.1
Classical definition
....................... 21
2.2
Examples
............................ 24
2.3
Combining likelihoods
..................... 27
2.4
Likelihood ratio
......................... 29
2.5
Maximum and curvature of likelihood
............ 30
2.6
Likelihood-based intervals
................... 35
2.7
Standard error and
Wald
statistic
............... 41
2.8
Invariance
principle
....................... 43
2.9
Practical implications of
invariance
principle
......... 45
2.10
Exercises
............................ 48
3
More properties of the likelihood
53
3.1
Sufficiency
............................ 53
3.2
Minimal sufficiency
....................... 55
3.3
Multiparameter models
.................... 58
3.4
Profile likelihood
........................ 61
3.5
Calibration in multiparameter case
.............. 64
3.6
Exercises
............................ 67
4
Basic models and simple applications
73
4.1
Binomial or Bernoulli models
................. 73
4.2
Binomial model with under- or overdispersion
........ 76
4.3
Comparing two proportions
.................. 78
4.4
Poisson
model
.......................... 82
4.5
Poisson
with overdispersion
.................. 84
4.6
Traffic deaths example
..................... 86
4.7
Aspirin data example
...................... 87
Contents
4.8
Continuous data
........................ 89
4.9
Exponential family
....................... 95
4.10
Box
-Сох
transformation family
................ 102
4.11
Location-scale family
...................... 104
4.12
Exercises
............................ 107
Frequentisi
properties
117
5.1
Bias of point estimates
..................... 117
5.2
Estimating and reducing bias
................. 119
5.3
Variability of point estimates
................. 123
5.4
Likelihood and P-value
..................... 125
5.5
CI
and coverage probability
.................. 128
5.6
Confidence density,
CI
and the bootstrap
.......... 131
5.7
Exact inference for
Poisson
model
............... 134
5.8
Exact inference for binomial model
.............. 139
5.9
Nuisance parameters
...................... 140
5.10
Criticism of CIs
......................... 142
5.11
Exercises
............................ 145
Modelling relationships: regression models
149
6.1
Normal linear models
...................... 150
6.2
Logistic regression models
................... 154
6.3
Poisson
regression models
................... 157
6.4
Nonnonnal continuous regression
............... 160
6.5
Exponential family regression models
............. 163
6.6
Deviance in GLM
........................ 166
6.7
Iterative weighted least squares
................ 174
6.8
Box Cox transformation family
................ 178
6.9
Location-scale regression models
............... 181
6.10
Exercises
............................ 187
Evidence and the likelihood principle*
193
7.1
Ideal inference machine?
.................... 193
7.2
Sufficiency and the likelihood principles
........... 194
7.3
Conditionality principle and ancillarity
............ 196
7.4
Birnbaum s theorem
...................... 197
7.5
Sequential experiments and stopping rule
.......... 199
7.6
Multiplicity
........................... 204
7.7
Questioning the likelihood principle
.............. 206
7.8
Exercises
............................ 211
Score function and Fisher information
213
8.1
Sampling variation of score function
............. 213
8.2
The mean of S(8)
........................ 215
8.3
The variance of
Ѕ(в)
...................... 216
8.4
Properties of expected Fisher information
.......... 219
Contents xi
8.5
Cramér-Rao
lower bound
................... 221
8.6
Minimum variance unbiased estimation*
........... 223
8.7
Multiparameter CRLB
..................... 226
8.8
Exercises
............................ 228
9
Large-sample results
231
9.1
Background results
....................... 231
9.2
Distribution of the score statistic
............... 235
9.3
Consistency of MLE for scalar
θ
............... 238
9.4
Distribution of MLE and the
Wald
statistic
......... 241
9.5
Distribution of likelihood ratio statistic
........... 243
9.6
Observed versus expected information*
............ 244
9.7
Proper variance of the score statistic*
............ 247
9.8
Higher-order approximation: magic formula*
........ 247
9.9
Multiparameter case:
θ
Є
BP ................. 256
9.10
Examples
............................ 259
9.11
Nuisance parameters
...................... 264
9.12
χ1
goodness-of-fit tests
..................... 268
9.13
Exercises
............................ 270
10
Dealing with nuisance parameters
273
10.1
Inconsistent likelihood estimates
............... 274
10.2
Ideal case: orthogonal parameters
............... 276
10.3
Marginal and conditional likelihood
.............. 278
10.4
Comparing
Poisson
means
................... 281
10.5
Comparing proportions
.................... 283
10.6
Modified profile likelihood*
.................. 286
10.7
Estimated likelihood
...................... 292
10.8
Exercises
............................ 294
11
Complex data structure
297
11.1
ARMA
models
......................... 297
11.2
Markov chains
......................... 299
11.3
Replicated Markov chains
................... 302
11.4
Spatial data
........................... 305
11.5
Censored/survival data
..................... 309
11.6
Survival regression models
................... 314
11.7
Hazard regression and Cox partial likelihood
........ 316
11.8
Poisson
point processes
.................... 320
11.9
Replicated
Poisson
processes
................. 324
ll.lODiscrete time model for
Poisson
processes
.......... 331
11.11
Exercises
............................ 335
12
EM Algorithm
341
12.1
Motivation
........................... 341
12.2
General specification
...................... 342
xii Contents
12.3
Exponential family model
................... 344
12.4
General properties
....................... 348
12.5
Mixture models
......................... 349
12.6
Robust estimation
....................... 352
12.7
Estimating infection pattern
.................. 354
12.8
Mixed model estimation*
................... 356
12.9
Standard errors
......................... 359
12.10Exercises
............................ 362
13
Robustness of likelihood specification
365
13.1
Analysis of Darwin s data
................... 365
13.2
Distance between model and the truth
........... 367
13.3
Maximum likelihood under a wrong model
.......... 370
13.4
Large-sample properties
.................... 372
13.5
Comparing working models with the AIC
.......... 375
13.6
Deriving the AIC
........................ 379
13.7
Exercises
............................ 383
14
Estimating equation and quasi-likelihood
385
14.1
Examples
............................ 387
14.2
Computing
β
in nonlinear cases
................ 390
14.3
Asymptotic distribution
.................... 393
14.4
Generalized estimating equation
............... 395
14.5
Robust estimation
....................... 398
14.6
Asymptotic Properties
..................... 404
15
Empirical likelihood
409
15.1
Profile likelihood
........................ 409
15.2
Double-bootstrap likelihood
.................. 413
15.3
BCa bootstrap likelihood
................... 415
15.4
Exponential family model
................... 418
15.5
General cases: M-estimation
.................. 420
15.6
Parametric
л^егѕиѕ
empirical likelihood
............ 422
15.7
Exercises
............................ 424
16
Likelihood of random parameters
425
16.1
The need to extend the likelihood
............... 425
16.2
Statistical prediction
...................... 427
16.3
Defining extended likelihood
.................. 429
16.4
Exercises
............................ 433
17
Random and mixed effects models
435
17.1
Simple random effects models
................. 436
17.2
Normal linear mixed models
.................. 439
17.3
Estimating genetic value from family data*
......... 442
17.4
Joint estimation of
β
and
b
.................. 444
Contents xiii
17.5 Computing
the variance component via
β
and
b.......
445
17.6
Examples
............................ 448
17.7
Extension to several random effects
.............. 452
17.8
Generalized linear mixed models
............... 458
17.9
Exact likelihood in GLMM
.................. 460
17.10Approximate likelihood in GLMM
.............. 462
lľ.HExercises
............................ 469
18
Nonparametric smoothing
473
18.1
Motivation
........................... 473
18.2
Linear mixed models approach
................ 477
18.3
Imposing smoothness using random effects model
...... 479
18.4
Penalized likelihood approach
................. 481
18.5
Estimate of
ƒ
given
σ2
and
σ
................ 482
18.6
Estimating the smoothing parameter
............. 485
18.7
Prediction intervals
....................... 489
18.8
Partial
lineai-
models
...................... 489
18.9
Smoothing nonequispaced data*
................ 490
le.lONon-Gaussian smoothing
.................... 492
lS.HNonparametric density estimation
.............. 497
18.12Nonnormal smoothness condition*
.............. 500
............................ 501
Bibliography
503
Index
515
|
| adam_txt |
Contents
1
Introduction
1
1.1
Prototype
of statistical problems
. 1
1.2
Statistical problems and their models
. 3
1.3
Statistical uncertainty: inevitable controversies
. 6
1.4
The emergence of statistics
. 8
1.5
Fisher and the third way
. 14
1.6
Exercises
. 19
2
Elements of likelihood inference
21
2.1
Classical definition
. 21
2.2
Examples
. 24
2.3
Combining likelihoods
. 27
2.4
Likelihood ratio
. 29
2.5
Maximum and curvature of likelihood
. 30
2.6
Likelihood-based intervals
. 35
2.7
Standard error and
Wald
statistic
. 41
2.8
Invariance
principle
. 43
2.9
Practical implications of
invariance
principle
. 45
2.10
Exercises
. 48
3
More properties of the likelihood
53
3.1
Sufficiency
. 53
3.2
Minimal sufficiency
. 55
3.3
Multiparameter models
. 58
3.4
Profile likelihood
. 61
3.5
Calibration in multiparameter case
. 64
3.6
Exercises
. 67
4
Basic models and simple applications
73
4.1
Binomial or Bernoulli models
. 73
4.2
Binomial model with under- or overdispersion
. 76
4.3
Comparing two proportions
. 78
4.4
Poisson
model
. 82
4.5
Poisson
with overdispersion
. 84
4.6
Traffic deaths example
. 86
4.7
Aspirin data example
. 87
Contents
4.8
Continuous data
. 89
4.9
Exponential family
. 95
4.10
Box
-Сох
transformation family
. 102
4.11
Location-scale family
. 104
4.12
Exercises
. 107
Frequentisi
properties
117
5.1
Bias of point estimates
. 117
5.2
Estimating and reducing bias
. 119
5.3
Variability of point estimates
. 123
5.4
Likelihood and P-value
. 125
5.5
CI
and coverage probability
. 128
5.6
Confidence density,
CI
and the bootstrap
. 131
5.7
Exact inference for
Poisson
model
. 134
5.8
Exact inference for binomial model
. 139
5.9
Nuisance parameters
. 140
5.10
Criticism of CIs
. 142
5.11
Exercises
. 145
Modelling relationships: regression models
149
6.1
Normal linear models
. 150
6.2
Logistic regression models
. 154
6.3
Poisson
regression models
. 157
6.4
Nonnonnal continuous regression
. 160
6.5
Exponential family regression models
. 163
6.6
Deviance in GLM
. 166
6.7
Iterative weighted least squares
. 174
6.8
Box Cox transformation family
. 178
6.9
Location-scale regression models
. 181
6.10
Exercises
. 187
Evidence and the likelihood principle*
193
7.1
Ideal inference machine?
. 193
7.2
Sufficiency and the likelihood principles
. 194
7.3
Conditionality principle and ancillarity
. 196
7.4
Birnbaum's theorem
. 197
7.5
Sequential experiments and stopping rule
. 199
7.6
Multiplicity
. 204
7.7
Questioning the likelihood principle
. 206
7.8
Exercises
. 211
Score function and Fisher information
213
8.1
Sampling variation of score function
. 213
8.2
The mean of S(8)
. 215
8.3
The variance of
Ѕ(в)
. 216
8.4
Properties of expected Fisher information
. 219
Contents xi
8.5
Cramér-Rao
lower bound
. 221
8.6
Minimum variance unbiased estimation*
. 223
8.7
Multiparameter CRLB
. 226
8.8
Exercises
. 228
9
Large-sample results
231
9.1
Background results
. 231
9.2
Distribution of the score statistic
. 235
9.3
Consistency of MLE for scalar
θ
. 238
9.4
Distribution of MLE and the
Wald
statistic
. 241
9.5
Distribution of likelihood ratio statistic
. 243
9.6
Observed versus expected information*
. 244
9.7
Proper variance of the score statistic*
. 247
9.8
Higher-order approximation: magic formula*
. 247
9.9
Multiparameter case:
θ
Є
BP . 256
9.10
Examples
. 259
9.11
Nuisance parameters
. 264
9.12
χ1
goodness-of-fit tests
. 268
9.13
Exercises
. 270
10
Dealing with nuisance parameters
273
10.1
Inconsistent likelihood estimates
. 274
10.2
Ideal case: orthogonal parameters
. 276
10.3
Marginal and conditional likelihood
. 278
10.4
Comparing
Poisson
means
. 281
10.5
Comparing proportions
. 283
10.6
Modified profile likelihood*
. 286
10.7
Estimated likelihood
. 292
10.8
Exercises
. 294
11
Complex data structure
297
11.1
ARMA
models
. 297
11.2
Markov chains
. 299
11.3
Replicated Markov chains
. 302
11.4
Spatial data
. 305
11.5
Censored/survival data
. 309
11.6
Survival regression models
. 314
11.7
Hazard regression and Cox partial likelihood
. 316
11.8
Poisson
point processes
. 320
11.9
Replicated
Poisson
processes
. 324
ll.lODiscrete time model for
Poisson
processes
. 331
11.11
Exercises
. 335
12
EM Algorithm
341
12.1
Motivation
. 341
12.2
General specification
. 342
xii Contents
12.3
Exponential family model
. 344
12.4
General properties
. 348
12.5
Mixture models
. 349
12.6
Robust estimation
. 352
12.7
Estimating infection pattern
. 354
12.8
Mixed model estimation*
. 356
12.9
Standard errors
. 359
12.10Exercises
. 362
13
Robustness of likelihood specification
365
13.1
Analysis of Darwin's data
. 365
13.2
Distance between model and the 'truth'
. 367
13.3
Maximum likelihood under a wrong model
. 370
13.4
Large-sample properties
. 372
13.5
Comparing working models with the AIC
. 375
13.6
Deriving the AIC
. 379
13.7
Exercises
. 383
14
Estimating equation and quasi-likelihood
385
14.1
Examples
. 387
14.2
Computing
β
in nonlinear cases
. 390
14.3
Asymptotic distribution
. 393
14.4
Generalized estimating equation
. 395
14.5
Robust estimation
. 398
14.6
Asymptotic Properties
. 404
15
Empirical likelihood
409
15.1
Profile likelihood
. 409
15.2
Double-bootstrap likelihood
. 413
15.3
BCa bootstrap likelihood
. 415
15.4
Exponential family model
. 418
15.5
General cases: M-estimation
. 420
15.6
Parametric
л^егѕиѕ
empirical likelihood
. 422
15.7
Exercises
. 424
16
Likelihood of random parameters
425
16.1
The need to extend the likelihood
. 425
16.2
Statistical prediction
. 427
16.3
Defining extended likelihood
. 429
16.4
Exercises
. 433
17
Random and mixed effects models
435
17.1
Simple random effects models
. 436
17.2
Normal linear mixed models
. 439
17.3
Estimating genetic value from family data*
. 442
17.4
Joint estimation of
β
and
b
. 444
Contents xiii
17.5 Computing
the variance component via
β
and
b.
445
17.6
Examples
. 448
17.7
Extension to several random effects
. 452
17.8
Generalized linear mixed models
. 458
17.9
Exact likelihood in GLMM
. 460
17.10Approximate likelihood in GLMM
. 462
lľ.HExercises
. 469
18
Nonparametric smoothing
473
18.1
Motivation
. 473
18.2
Linear mixed models approach
. 477
18.3
Imposing smoothness using random effects model
. 479
18.4
Penalized likelihood approach
. 481
18.5
Estimate of
ƒ
given
σ2
and
σ\
. 482
18.6
Estimating the smoothing parameter
. 485
18.7
Prediction intervals
. 489
18.8
Partial
lineai-
models
. 489
18.9
Smoothing nonequispaced data*
. 490
le.lONon-Gaussian smoothing
. 492
lS.HNonparametric density estimation
. 497
18.12Nonnormal smoothness condition*
. 500
. 501
Bibliography
503
Index
515 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Pawitan, Yudi |
| author_facet | Pawitan, Yudi |
| author_role | aut |
| author_sort | Pawitan, Yudi |
| author_variant | y p yp |
| building | Verbundindex |
| bvnumber | BV023273710 |
| classification_rvk | MR 2100 QH 170 SK 840 |
| ctrlnum | (OCoLC)255695874 (DE-599)BVBBV023273710 |
| 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 | Soziologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 1. publ., [Nachdr.] |
| format | Book |
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| id | DE-604.BV023273710 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:37:01Z |
| indexdate | 2024-07-09T21:14:41Z |
| institution | BVB |
| isbn | 9780198507659 0198507658 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016458663 |
| oclc_num | 255695874 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| physical | XIII, 528 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford science publication |
| spelling | Pawitan, Yudi Verfasser aut In all likelihood statistical modelling and inference using likelihood Yudi Pawitan 1. publ., [Nachdr.] Oxford [u.a.] Oxford Univ. Press 2007 XIII, 528 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publication Likelihood-Funktion Maximum-Likelihood-Schätzung Wahrscheinlichkeitsrechnung - Statistisches Modell Likelihood-Funktion (DE-588)4657256-9 gnd rswk-swf Likelihood-Funktion (DE-588)4657256-9 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016458663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pawitan, Yudi In all likelihood statistical modelling and inference using likelihood Likelihood-Funktion Maximum-Likelihood-Schätzung Wahrscheinlichkeitsrechnung - Statistisches Modell Likelihood-Funktion (DE-588)4657256-9 gnd |
| subject_GND | (DE-588)4657256-9 |
| title | In all likelihood statistical modelling and inference using likelihood |
| title_auth | In all likelihood statistical modelling and inference using likelihood |
| title_exact_search | In all likelihood statistical modelling and inference using likelihood |
| title_exact_search_txtP | In all likelihood statistical modelling and inference using likelihood |
| title_full | In all likelihood statistical modelling and inference using likelihood Yudi Pawitan |
| title_fullStr | In all likelihood statistical modelling and inference using likelihood Yudi Pawitan |
| title_full_unstemmed | In all likelihood statistical modelling and inference using likelihood Yudi Pawitan |
| title_short | In all likelihood |
| title_sort | in all likelihood statistical modelling and inference using likelihood |
| title_sub | statistical modelling and inference using likelihood |
| topic | Likelihood-Funktion Maximum-Likelihood-Schätzung Wahrscheinlichkeitsrechnung - Statistisches Modell Likelihood-Funktion (DE-588)4657256-9 gnd |
| topic_facet | Likelihood-Funktion Maximum-Likelihood-Schätzung Wahrscheinlichkeitsrechnung - Statistisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016458663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pawitanyudi inalllikelihoodstatisticalmodellingandinferenceusinglikelihood |