Probability, statistics and econometrics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London, United Kingdom
Academic Press
[2017]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xix, 367 Seiten Illustrationen |
| ISBN: | 0128104953 9780128104958 |
Internformat
MARC
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| 245 | 1 | 0 | |a Probability, statistics and econometrics |c Oliver Linton (University of Cambridge, United Kingdom) |
| 264 | 1 | |a London, United Kingdom |b Academic Press |c [2017] | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
List of Figures xiii
About the Author xv
Preface xv ii
Acknowledgment xix
Part I
Probability and Distribution
1. Probability Theory
1.1 Introduction 3
1.2 Definition of Probability 4
1.3 Some Counting Problems 7
2. Conditional Probability and Independence
2.1 Conditional Probability 11
2.2 Bayes Theorem 12
2.3 Independence 14
3. Random Variables, Distribution Functions, and
Densities
3.1 Random Variables 21
3.2 Distribution Functions 23
3.3 Quantile 27
3.4 Density and Mass Functions 31
4. Transformations of Random Variables
4.1 Distributions of Functions of a Random Variable 35
4.2 Probability Integral Transform 40
vii
vii։ Contents
5. The Expectation
5.1 Definition and Properties 43
5.2 Additional Moments and Cumulants 49
5.3 An Interpretation of Expectation and Median 52
6. Examples of Univariate Distributions
6.1 Parametric Families of Distributions 55
6.1.1 Discrete Distributions 55
6.1.2 Continuous Distributions 58
7. Multivariate Random Variables
7.1 Multivariate Distributions 63
7.2 Conditional Distributions and Independence 66
7.3 Covariance 69
7.4 Conditional Expectation and the Regression Function 72
7.5 Examples 81
7.6 Multivariate Transformations 85
7.6.1 Some Special Cases Where q = 1 and p = 2 87
7.6.2 Copula 90
8. Asymptotic Theory
8.1 inequalities 93
8.2 Notions of Convergence 96
8.3 Laws of Large Numbers and CLT 100
8.3.1 Gambling Model 103
8.4 Some Additional Tools 1 05
9. Exercises and Complements
Part II
Statistics
10. Introduction
10.1 Sampling Theory 135
10.2 Sample Statistics 136
1 0.2.1 Properties of Descriptive Statistics 1 38
10.2.2 Exact Properties Specific to the Normal Distribution 140
10.3 Statistical Principles 142
10.3.1 Some Important Concepts 144
10.3.2 Bayesian Methods 146
Contents ¡X
11. Estimation Theory
11.1 Estimation Methods 151
11.1.1 The Original Method of Moments or Analogy Principle 151
11.1.2 Maximum Likelihood 155
11.1.3 Computation 160
11.2 Comparison of Estimators and Optimality 1 63
11.2.1 Asymptotic Properties 170
11.3 Robustness and Other Issues with the MLE 172
12. Hypothesis Testing
12.1 Hypotheses 175
12.2 Test Procedure 176
12.3 Likelihood Tests 181
12.4 Power of Tests 184
12.4.1 Neyman Pearson Optimal Testing 186
12.4.2 Consistency of Tests and Local Power 189
12.4.3 Nonparametric Testing 193
12.5 Criticisms of the Standard Hypothesis Testing Approach 196
13. Confidence Intervals and Sets
13.1 Definitions 199
1 3.1.1 General Large Sample Setting 201
13.2 Likelihood Ratio Confidence Interval 203
13.2.1 A Bayesian Interval 208
13.3 Methods of Evaluating Intervals 209
14. Asymptotic Tests and the Bootstrap
14.1 Simulation Methods 211
14.2 Bootstrap 212
14.2.1 Subsampling 219
15. Exercises and Complements
Part Ml
Econometrics
16. Linear Algebra
16.1 Matrices 231
16.1.1 Linear Spaces 236
16.1.2 Eigenvectors and Eigenvalues 237
16.1.3 Applications 244
16.2 Systems of Linear Equations and Projection 249
x Contents
17. The Least Squares Procedure
17.1 Projection Approach 251
17.2 Partitioned Regression 255
17.3 Restricted Least Squares 257
17.3.1 Backfitting in Linear Regression 259
1 7.3.2 Goodness of Fit 261
18. Linear Model
18.1 Introduction 263
18.2 The Model 263
19. Statistical Properties of the OLS Estimator
19.1 Properties of OLS 267
19.1.1 Alternative Estimators 271
19.2 Optimality 271
20. Hypothesis Testing for Linear Regression
20.1 Hypotheses of Interest 277
20.2 Test of a Single Linear Hypothesis 278
20.3 Test of Multiple Linear Hypothesis 280
20.4 Test of Multiple Linear Hypothesis Based on Fit 281
20.5 Likelihood Based Testing 285
20.6 Bayesian Approach 287
21. Omission of Relevant Variables, Inclusion of Irrelevant
Variables, and Model Selection
21.1 Omission of Relevant Variables 289
21.2 Inclusion of Irrelevant Variables/Knowledge of Parameters 291
21.3 Model Selection 292
21.3.1 Problems and Issues 293
21.4 Lasso 294
22. Asymptotic Properties of OLS Estimator and Test
Statistics
22.1 The I.I.D. Case 297
22.2 The Non-I.I.D. Case 302
23. Generalized Method of Moments and Extremum
Estimators
23.1 Generalized Method Moments 313
Contents XI
23.2 Asymptotic Properties of Extremum Estimators 316
23.2.1 Consistency 316
23.2.2 Asymptotic Normality 322
23.3 Quantile Regression 32 7
24. A Nonparametric Postscript
25. A Case Study
26. Exercises and Complements
Appendix
A Some Results from Calculus 357
B Some Matrix Facts 358
B.1 Matrix Operations Satisfy Certain Mathematical Laws 358
B.2 Transpose of a Matrix 358
B.3 Inverse 358
B.4 Trace of a Matrix 358
B.5 Determinant of a Matrix 358
B.6 Rank of a Matrix 359
B.7 Eigenvalues of Real Symmetric Matrix 359
B.8 Positive Definiteness 359
Bibliography 361
Index 363
|
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| illustrated | Illustrated |
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| institution | BVB |
| isbn | 0128104953 9780128104958 |
| language | English |
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| physical | xix, 367 Seiten Illustrationen |
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| spelling | Linton, Oliver Verfasser (DE-588)171218221 aut Probability, statistics and econometrics Oliver Linton (University of Cambridge, United Kingdom) London, United Kingdom Academic Press [2017] xix, 367 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematical statistics Ökonometrie (DE-588)4132280-0 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Ökonometrie (DE-588)4132280-0 s Wahrscheinlichkeit (DE-588)4137007-7 s Statistik (DE-588)4056995-0 s DE-604 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029749844&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Linton, Oliver Probability, statistics and econometrics Mathematical statistics Ökonometrie (DE-588)4132280-0 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4132280-0 (DE-588)4137007-7 (DE-588)4056995-0 |
| title | Probability, statistics and econometrics |
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| title_exact_search | Probability, statistics and econometrics |
| title_full | Probability, statistics and econometrics Oliver Linton (University of Cambridge, United Kingdom) |
| title_fullStr | Probability, statistics and econometrics Oliver Linton (University of Cambridge, United Kingdom) |
| title_full_unstemmed | Probability, statistics and econometrics Oliver Linton (University of Cambridge, United Kingdom) |
| title_short | Probability, statistics and econometrics |
| title_sort | probability statistics and econometrics |
| topic | Mathematical statistics Ökonometrie (DE-588)4132280-0 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematical statistics Ökonometrie Wahrscheinlichkeit Statistik |
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