Probability Theory and Statistical Inference : Econometric Modelling with Observational Data

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Probability Theory and Statistical Inference : Econometric Modelling with Observational Data

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  • 製本 Hardcover:ハードカバー版/ページ数 815 p.
  • 言語 ENG,ENG
  • 商品コード 9780521413541
  • DDC分類 330.015195

Table of Contents

Preface                                            xi  (13)
Acknowledgments xxiv
1 An introduction to empirical modeling 1 (30)
1.1 Introduction 1 (2)
1.2 Stochastic phenomena, a preliminary 3 (10)
view
1.3 Chance regularity and statistical 13 (3)
models
1.4 Statistical adequacy 16 (3)
1.5 Statistical versus theory information* 19 (1)
1.6 Observed data 20 (9)
1.7 Looking ahead 29 (1)
1.8 Exercises 30 (1)
2 Probability theory: a modeling framework 31 (46)
2.1 Introduction 31 (2)
2.2 Simple statistical model: a 33 (6)
preliminary view
2.3 Probability theory: an introduction 39 (3)
2.4 Random experiments 42 (3)
2.5 Formalizing condition [a]: the 45 (3)
outcomes set
2.6 Formalizing condition [b]: events and 48 (21)
probabilities
2.7 Formalizing condition [c]: random 69 (4)
trials
2.8 Statistical space 73 (1)
2.9 A look forward 74 (1)
2.10 Exercises 75 (2)
3 The notion of a probability model 77 (68)
3.1 Introduction 77 (1)
3.2 The notion of a simple random variable 78 (7)
3.3 The general notion of a random variable 85 (4)
3.4 The cumulative distribution and 89 (8)
density functions
3.5 From a probability space to a 97 (7)
probability model
3.6 Parameters and moments 104 (5)
3.7 Moments 109 (22)
3.8 Inequalities 131 (1)
3.9 Summary 132 (1)
3.10 Exercises 133 (2)
Appendix A Univariate probability models 135 (10)
A.1 Discrete univariate distributions 136 (2)
A.2 Continuous univariate distributions 138 (7)
4 The notion of a random sample 145 (45)
4.1 Introduction 145 (2)
4.2 Joint distributions 147 (8)
4.3 Marginal distributions 155 (3)
4.4 Conditional distributions 158 (9)
4.5 Independence 167 (4)
4.6 Identical distributions 171 (4)
4.7 A simple statistical model in 175 (6)
empirical modeling: a preliminary view
4.8 Ordered random samples* 181 (3)
4.9 Summary 184 (1)
4.10 Exercises 184 (1)
Appendix B Bivariate distributions 185 (5)
B.1 Discrete bivariate distributions 185 (1)
B.2 Continuous bivariate distributions 186 (4)
5 Probabilistic concepts and real data 190 (70)
5.1 Introduction 190 (3)
5.2 Early developments 193 (2)
5.3 Graphic displays: a t-plot 195 (2)
5.4 Assessing distribution assumptions 197 (15)
5.5 Independence and the t-plot 212 (5)
5.6 Homogeneity and the t-plot 217 (12)
5.7 The empirical cdf and related graphs* 229 (25)
5.8 Generating pseudo-random numbers* 254 (4)
5.9 Summary 258 (1)
5.10 Exercises 259 (1)
6 The notion of a non-random sample 260 (77)
6.1 Introduction 260 (3)
6.2 Non-random sample: a preliminary view 263 (6)
6.3 Dependence between two random 269 (3)
variables: joint distributions
6.4 Dependence between two random 272 (10)
variables: moments
6.5 Dependence and the measurement system 282 (8)
6.6 Joint distributions and dependence 290 (19)
6.7 From probabilistic concepts to 309 (21)
observed data
6.8 What comes next? 330 (5)
6.9 Exercises 335 (2)
7 Regression and related notions 337 (63)
7.1 Introduction 337 (2)
7.2 Conditioning and regression 339 (17)
7.3 Reduction and stochastic conditioning 356 (10)
7.4 Weak exogeneity* 366 (2)
7.5 The notion of a statistical generating 368 (9)
mechanism (GM)
7.6 The biometric tradition in statistics 377 (20)
7.7 Summary 397 (1)
7.8 Exercises 397 (3)
8 Stochastic processes 400 (62)
8.1 Introduction 400 (3)
8.2 The notion of a stochastic process 403 (7)
8.3 Stochastic processes: a preliminary 410 (10)
view
8.4 Dependence restrictions 420 (6)
8.5 Homogeneity restrictions 426 (5)
8.6 "Building block" stochastic processes 431 (2)
8.7 Markov processes 433 (2)
8.8 Random walk processes 435 (3)
8.9 Martingale processes 438 (6)
8.10 Gaussian processes 444 (14)
8.11 Point processes 458 (2)
8.12 Exercises 460 (2)
9 Limit theorems 462 (50)
9.1 Introduction to limit theorems 462 (3)
9.2 Tracing the roots of limit theorems 465 (4)
9.3 The Weak Law of Large Numbers 469 (7)
9.4 The Strong Law of Large Numbers 476 (5)
9.5 The Law of Iterated Logarithm* 481 (1)
9.6 The Central Limit Theorem 482 (9)
9.7 Extending the limit theorems* 491 (4)
9.8 Functional Central Limit Theorem* 495 (8)
9.9 Modes of convergence 503 (7)
9.10 Summary and conclusion 510 (1)
9.11 Exercises 510 (2)
10 From probability theory to statistical 512 (46)
inference*
10.1 Introduction 512 (2)
10.2 Interpretations of probability 514 (6)
10.3 Attempts to build a bridge between 520 (8)
probability and observed data
10.4 Toward a tentative bridge 528 (13)
10.5 The probabilistic reduction approach 541 (5)
to specification
10.6 Parametric versus non-parametric 546 (10)
models
10.7 Summary and conclusions 556 (1)
10.8 Exercises 556 (2)
11 An introduction to statistical inference 558 (44)
11.1 Introduction 558 (1)
11.2 An introduction to the classical 559 (9)
approach
11.3 The classical versus the Bayesian 568 (2)
approach
11.4 Experimental versus observational data 570 (5)
11.5 Neglected facets of statistical 575 (3)
inference
11.6 Sampling distributions 578 (6)
11.7 Functions of random variables 584 (10)
11.8 Computer intensive techniques for 594 (6)
approximating sampling distributions*
11.9 Exercises 600 (2)
12 Estimation I: Properties of estimators 602 (35)
12.1 Introduction 602 (1)
12.2 Defining an estimator 603 (4)
12.3 Finite sample properties 607 (8)
12.4 Asymptotic properties 615 (6)
12.5 The simple Normal model 621 (6)
12.6 Sufficient statistics and optimal 627 (8)
estimators*
12.7 What comes next? 635 (1)
12.8 Exercises 635 (2)
13 Estimation II: Methods of estimation 637 (44)
13.1 Introduction 637 (2)
13.2 Moment matching principle 639 (9)
13.3 The least-squares method 648 (6)
13.4 The method of moments 654 (5)
13.5 The maximum likelihood method 659 (19)
13.6 Exercises 678 (3)
14 Hypothesis testing 681 (48)
14.1 Introduction 681 (1)
14.2 Leading up to the Fisher approach 682 (10)
14.3 The Neyman-Pearson framework 692 (21)
14.4 Asymptotic test procedures* 713 (7)
14.5 Fisher versus Neyman-Pearson 720 (7)
14.6 Conclusion 727 (1)
14.7 Exercises 727 (2)
15 Misspecification testing 729 (58)
15.1 Introduction 729 (4)
15.2 Misspecification testing: formulating 733 (6)
the problem
15.3 A smorgasbord of misspecification 739 (14)
tests
15.4 The probabilistic reduction approach 753 (12)
and misspecification
15.5 Empirical examples 765 (18)
15.6 Conclusion 783 (1)
15.7 Exercises 784 (3)
References 787 (19)
Index 806