Probability Theory and Statistical Inference Econometric Modeling with Observational Data

A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication data Spanos, Aris, 1952– Probability Theory and Statistical Inference: econometric modeling with observational data / Aris Spanos p. cm. Includes bibliographical references (p.) and index. Contents Preface page xi Acknowledgments xxiv 1 An introduction to empirical modeling 1 1.1 Introduction 1 1.2 Stochastic phenomena, a preliminary view 3 1.3 Chance regularity and statistical models 13 1.4 Statistical adequacy 16 1.5 Statistical versus theory information* 19 1.6 Observed data 20 1.7 Looking ahead 29 1.8 Exercises 30 2 Probability theory: a modeling framework 31 2.1 Introduction 31 2.2 Simple statistical model: a preliminary view 33 2.3 Probability theory: an introduction 39 2.4 Random experiments 42 2.5 Formalizing condition [a]: the outcomes set 45 2.6 Formalizing condition [b]: events and probabilities 48 2.7 Formalizing condition [c]: random trials 69 2.8 Statistical space 73 2.9 A look forward 74 2.10 Exercises 75 3 The notion of a probability model 77 3.1 Introduction 77 3.2 The notion of a simple random variable 78 3.3 The general notion of a random variable 85 3.4 The cumulative distribution and density functions 89 v 3.5 From a probability space to a probability model Appendix A Univariate probability models 135 A.1 Discrete univariate distributions 136 A.2 Continuous univariate distributions 138 4 The notion of a random sample 145 4.1 Introduction 145 4.2 Joint distributions 147 4.3 Marginal distributions 155 4.4 Conditional distributions 158 4.5 Independence 167 4.6 Identical distributions 171 4.7 A simple statistical model in empirical modeling: a preliminary view 175 4.8 Ordered random samples* 181 4.9 Summary 184 4.10 Exercises 184 Appendix B Bivariate distributions 185 B.1 Discrete bivariate distributions 185 B.2 Continuous bivariate distributions 186