Format:
1 online resource (843 pages)
Edition:
1st ed.
ISBN:
9780521413541
,
9780511152139
Content:
This major textbook is intended for students taking introductory courses in Probability Theory and Statistical Inference. The text is extremely student-friendly, with pathways designed for semester usage, and although aimed primarily at students of econometrics and economics, will have considerable utility for courses in all disciplines using observational data
Note:
Intro -- Contents -- Preface -- Acknowledgments -- Symbols -- Acronyms -- 1 An introduction to empirical modeling -- 1.1 Introduction -- 1.2 Stochastic phenomena, a preliminary view -- 1.3 Chance regularity and statistical models -- 1.4 Statistical adequacy -- 1.5 Statistical versus theory information* -- 1.6 Observed data -- 1.7 Looking ahead -- 1.8 Exercises -- 2 Probability theory: a modeling framework -- 2.1 Introduction -- 2.2 Simple statistical model: a preliminary view -- 2.3 Probability theory: an introduction -- 2.4 Random experiments -- 2.5 Formalizing condition [a]: the outcomes set -- 2.6 Formalizing condition [b]: events and probabilities -- 2.7 Formalizing condition [c]: random trials -- 2.8 Statistical space -- 2.9 A look forward -- 2.10 Exercises -- 3 The notion of a probability model -- 3.1 Introduction -- 3.2 The notion of a simple random variable -- 3.3 The general notion of a random variable -- 3.4 The cumulative distribution and density functions -- 3.5 From a probability space to a probability model -- 3.6 Parameters and moments -- 3.7 Moments -- 3.8 Inequalities -- 3.9 Summary -- 3.10 Exercises -- Appendix A Univariate probability models -- A.1 Discrete univariate distributions -- A.2 Continuous univariate distributions -- 4 The notion of a random sample -- 4.1 Introduction -- 4.2 Joint distributions -- 4.3 Marginal distributions -- 4.4 Conditional distributions -- 4.5 Independence -- 4.6 Identical distributions -- 4.7 A simple statistical model in empirical modeling: a preliminary view -- 4.8 Ordered random samples* -- 4.9 Summary -- 4.10 Exercises -- Appendix B Bivariate distributions -- B.1 Discrete bivariate distributions -- B.2 Continuous bivariate distributions -- 5 Probabilistic concepts and real data -- 5.1 Introduction -- 5.2 Early developments -- 5.3 Graphical displays: a t-plot
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10.3 Attempts to build a bridge between probability and observed data -- 10.4 Toward a tentative bridge -- 10.5 The probabilistic reduction approach to specification -- 10.6 Parametric versus non-parametric models -- 10.7 Summary and conclusions -- 10.8 Exercises -- 11 An introduction to statistical inference -- 11.1 Introduction -- 11.2 An introduction to the classical approach -- 11.3 The classical versus the Bayesian approach -- 11.4 Experimental versus observational data -- 11.5 Neglected facets of statistical inference -- 11.6 Sampling distributions -- 11.7 Functions of random variables -- 11.8 Computer intensive techniques for approximating sampling distributions* -- 11.9 Exercises -- 12 Estimation I: Properties of estimators -- 12.1 Introduction -- 12.2 Defining an estimator -- 12.3 Finite sample properties -- 12.4 Asymptotic properties -- 12.5 The simple Normal model -- 12.6 Sufficient statistics and optimal estimators* -- 12.7 What comes next? -- 12.8 Exercises -- 13 Estimation II: Methods of estimation -- 13.1 Introduction -- 13.2 Moment matching principle -- 13.3 The least-squares method -- 13.4 The method of moments -- 13.5 The maximum likelihood method -- 13.6 Exercises -- 14 Hypothesis testing -- 14.1 Introduction -- 14.2 Leading up to the Fisher approach -- 14.3 The Neyman-Pearson framework -- 14.4 Asymptotic test procedures* -- 14.5 Fisher versus Neyman-Pearson -- 14.6 Conclusion -- 14.7 Exercises -- 15 Misspecification testing -- 15.1 Introduction -- 15.2 Misspecification testing: formulating the problem -- 15.3 A smorgasbord of misspecification tests -- 15.4 The probabilistic reduction approach and misspecification -- 15.5 Empirical examples -- 15.6 Conclusion -- 15.7 Exercises -- References -- Index
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5.4 Assessing distribution assumptions -- 5.5 Independence and the t-plot -- 5.6 Homogeneity and the t-plot -- 5.7 The empirical cdf and related graphs* -- 5.8 Generating pseudo-random numbers* -- 5.9 Summary -- 5.10 Exercises -- 6 The notion of a non-random sample -- 6.1 Introduction -- 6.2 Non-random sample: a preliminary view -- 6.3 Dependence between two random variables: joint distributions -- 6.4 Dependence between two random variables: moments -- 6.5 Dependence and the measurement system -- 6.6 Joint distributions and dependence -- 6.7 From probabilistic concepts to observed data -- 6.8 What comes next? -- 6.9 Exercises -- 7 Regression and related notions -- 7.1 Introduction -- 7.2 Conditioning and regression -- 7.3 Reduction and stochastic conditioning -- 7.4 Weak exogeneity* -- 7.5 The notion of a statistical generating mechanism (GM) -- 7.6 The biometric tradition in statistics -- 7.7 Summary -- 7.8 Exercises -- 8 Stochastic processes -- 8.1 Introduction -- 8.2 The notion of a stochastic process -- 8.3 Stochastic processes: a preliminary view -- 8.4 Dependence restrictions -- 8.5 Homogeneity restrictions -- 8.6 "Building block" stochastic processes -- 8.7 Markov processes -- 8.8 Random walk processes -- 8.9 Martingale processes -- 8.10 Gaussian processes -- 8.11 Point processes -- 8.12 Exercises -- 9 Limit theorems -- 9.1 Introduction to limit theorems -- 9.2 Tracing the roots of limit theorems -- 9.3 The Weak Law of Large Numbers -- 9.4 The Strong Law of Large Numbers -- 9.5 The Law of Iterated Logarithm* -- 9.6 The Central Limit Theorem -- 9.7 Extending the limit theorems* -- 9.8 Functional Central Limit Theorem* -- 9.9 Modes of convergence -- 9.10 Summary and conclusion -- 9.11 Exercises -- 10 From probability theory to statistical inference* -- 10.1 Introduction -- 10.2 Interpretations of probability
Additional Edition:
Print version Spanos, Aris Probability Theory and Statistical Inference Cambridge : Cambridge University Press,c1999 ISBN 9780521413541
Language:
English
Keywords:
Electronic books
URL:
FULL
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