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Home » Economic » Econometrics

Introduction to the Mathematical and Statistical Foundations of ...

Source: econ.la.psu.edu
Topic: Econometrics

Sort Desciption: econometrics or in a field course in econometric theory. ... developed during the period 1997-2003 for the first semester econometrics course Introduction ...

Content Inside: 1 Introduction to the Mathematical and Statistical Foundations of Econometrics Herman J. Bierens Pennsylvania State University November 13 2003 Revised: March 15 2004 2 Contents Preface Chapter 1: Probability and Measure 1.1. The Texas lotto 1.1.1 Introduction 1.1.2 Binomial numbers 1.1.3 Sample space 1.1.4 Algebras and sigma-algebras of events 1.1.5 Probability measure 1.2. Quality control 1.2.1 Sampling without replacement 1.2.2 Quality control in practice 1.2.3 Sampling with replacement 1.2.4 Limits of the hypergeometric and binomial probabilities 1.3. Why do we need sigma-algebras of events? 1.4. Properties of algebras and sigma-algebras 1.4.1 General properties 1.4.2 Borel sets 1.5. Properties of probability measures 1.6. The uniform probability measure 1.6.1 Introduction 1.6.2 Outer measure 1.7. Lebesgue measure and Lebesgue integral 1.7.1 Lebesgue measure 1.7.2 Lebesgue integral 1.8. Random variables and their distributions 3 1.8.1 Random variables and vectors 1.8.2 Distribution functions 1.9. Density functions 1.10. Conditional probability Bayes' rule and independence 1.10.1 Conditional probability 1.10.2 Bayes' rule 1.10.3 Independence 1.11. Exercises Appendixes: 1.A. Common structure of the proofs of Theorems 1.6 and 1.10 1.B. Extension of an outer measure to a probability measure Chapter 2: Borel Measurability Integration and Mathematical Expectations 2.1. Introduction 2.2. Borel measurability 2.3. Integrals of Borel measurable functions with respect to a probability measure 2.4. General measurability and integrals of random variables with respect to probability measures 2.5. Mathematical expectation 2.6. Some useful inequalities involving mathematical expectations 2.6.1 Chebishev's inequality 2.6.2 Holder's inequality 2.6.3 Liapounov's inequality 2.6.4 Minkowski's inequality 2.6.5 Jensen's inequality 2.7. Expectations of products of independent random variabl ...

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