This major new textbook is intended for students taking introductory courses in probability theory and statistical inference. The primary objective of this book is to establish the framework for the empirical modeling of observational (nonexperimental) data. The text is extremely student friendly, with pathways designed for semester usage, and although aimed primarily at students at second-year undergraduate level and above studying econometrics and economics, Probability Theory and Statistical Inference will also be useful for students in other disciplines that make extensive use of observational data, including finance, biology, sociology and psychology.
Author(s): Aris Spanos
Publisher: Cambridge University Press
Year: 1999
Language: English
Pages: 842
Title
......Page 3
Copyright
......Page 4
Contents......Page 5
Preface
......Page 10
Acknowledgments
......Page 23
Symbols
......Page 25
Acronyms
......Page 27
1.1 Introduction
......Page 28
1.2 Stochastic phenomena, a preliminary view
......Page 30
1.3 Chance regularity and statistical models
......Page 40
1.4 Statistical adequacy
......Page 43
1.5 Statistical versus theory information
......Page 46
1.6 Observed data
......Page 47
1.7 Looking ahead
......Page 56
1.8 Exercises
......Page 57
2.1 Introduction
......Page 58
2.2 Simple statistical model: a preliminary view
......Page 60
2.3 Probability theory: an introduction
......Page 66
2.4 Random experiments
......Page 69
2.5 Formalizing condition [a]: the outcomes set
......Page 72
2.6 Formalizing condition [b]: events and probabilities
......Page 75
2.7 Formalizing condition [c]: random trials
......Page 96
2.8 Statistical space
......Page 100
2.9 A look forward
......Page 101
2.10 Exercises
......Page 102
3.1 Introduction
......Page 104
3.2 The notion of a simple random sample
......Page 105
3.3 The general notion of a random variable
......Page 112
3.4 The cumulative distribution and density functions......Page 116
3.5 From a probability space to a probability model
......Page 124
3.6 Parameters and moments
......Page 131
3.7 Moments
......Page 136
3.8 Inequalities
......Page 158
3.9 Summary
......Page 159
3.10 Exercises
......Page 160
Appendix A Univariate probability models
......Page 162
4.1 Introduction
......Page 172
4.2 Joint distributions
......Page 174
4.3 Marginal distributions
......Page 182
4.4 Conditional distributions
......Page 185
4.5 Independence
......Page 194
4.6 Identical distributions
......Page 198
4.7 A simple statistical model in empirical modeling: a preliminary view
......Page 202
4.8 Ordered random samples
......Page 208
4.10 Exercises
......Page 211
Appendix B Bivariate distributions
......Page 212
5.1 Introduction
......Page 217
5.2 Early developments
......Page 220
5.3 Graphical displays: a t-plot
......Page 222
5.4 Assessing distribution assumptions
......Page 224
5.5 Independence and the t-plot
......Page 239
5.6 Homogeneity and the t-plot
......Page 244
5.7 The empirical cdf and related graphs
......Page 256
5.8 Generating pseudo-random numbers
......Page 281
5.9 Summary
......Page 285
5.10 Exercises
......Page 286
6.1 Introduction
......Page 287
6.2 Non-random sample: a preliminary view
......Page 290
6.3 Dependence between two random variables: joint distributions
......Page 296
6.4 Dependence between two random variables: moments
......Page 299
6.5 Dependence and the measurement system
......Page 309
6.6 Joint distributions and dependence
......Page 317
6.7 From probabilistic concepts to observed data
......Page 336
6.8 What comes next?
......Page 357
6.9 Exercises
......Page 362
7.1 Introduction
......Page 364
7.2 Conditioning and regression
......Page 366
7.3 Reduction and stochastic conditioning
......Page 383
7.4 Weak exogeneity
......Page 393
7.5 The notion of a statistical generating mechanism (GM)
......Page 395
7.6 The biometric tradition in statistics
......Page 404
7.8 Exercises
......Page 424
8.1 Introduction
......Page 427
8.2 The notion of a stochastic process
......Page 430
8.3 Stochastic processes: a preliminary view
......Page 437
8.4 Dependence restrictions
......Page 447
8.5 Homogeneity restrictions
......Page 453
8.6 "Building block" stochastic processes
......Page 458
8.7 Markov processes
......Page 460
8.8 Random walk processes
......Page 462
8.9 Martingale processes
......Page 465
8.10 Gaussian processes
......Page 471
8.11 Point processes
......Page 485
8.12 Exercises
......Page 487
9.1 Introduction to limit theorems
......Page 489
9.2 Tracing the roots of limit theorems
......Page 492
9.3 The Weak Law of Large Numbers
......Page 496
9.4 The Strong Law of Large Numbers
......Page 503
9.5 The Law of Iterated Logarithm
......Page 508
9.6 The Central Limit Theorem
......Page 509
9.7 Extending the limit theorems
......Page 518
9.8 Functional Central Limit Theorem
......Page 522
9.9 Modes of convergence
......Page 530
9.11 Exercises
......Page 537
10.1 Introduction
......Page 539
10.2 Interpretations of probability
......Page 541
10.3 Attempts to build a bridge between probability and observed data......Page 547
10.4 Toward a tentative bridge
......Page 555
10.5 The probabilistic approach to specification
......Page 568
10.6 Parametric versus non-parametric models
......Page 573
10.8 Exercises
......Page 583
11.1 Introduction
......Page 585
11.2 An introduction to the classical approach
......Page 586
11.3 The classical versus the Bayesian approach
......Page 595
11.4 Experimental versus observational data
......Page 597
11.5 Neglected facets of statistical inference
......Page 602
11.6 Sampling distributions
......Page 605
11.7 Functions of random variables
......Page 611
11.8 Computer intensive techniques for approximating sampling distributions
......Page 621
11.9 Exercises
......Page 627
12.1 Introduction
......Page 629
12.2 Defining an estimator
......Page 630
12.3 Finite sample properties
......Page 634
12.4 Asymptotic properties
......Page 642
12.5 The simple Normal model
......Page 648
12.6 Sufficient statistics and optimal estimators
......Page 654
12.8 Exercises
......Page 662
13.1 Introduction
......Page 664
13.2 Moment matching principle
......Page 666
13.3 The least-squares method
......Page 675
13.4 The method of moments
......Page 681
13.5 The maximum likelihood method
......Page 686
13.6 Exercises
......Page 705
14.1 Introduction
......Page 708
14.2 Leading up to the Fisher approach
......Page 709
14.3 The Neyman-Pearson framework
......Page 719
14.4 Asymptotic test procedures
......Page 740
14.5 Fisher versus Neyman-Pearson
......Page 747
14.7 Exercises
......Page 754
15.1 Introduction
......Page 756
15.2 Misspecification testing: formulating the problem
......Page 760
15.3 A smorgasbord of misspecification tests
......Page 766
15.4 The probabilistic reduction approach and misspecification
......Page 780
15.5 Empirical examples
......Page 792
15.6 Conclusion
......Page 810
15.7 Exercises
......Page 811
References
......Page 814
Index
......Page 833
