Course detail

LES5727 - Applied Statistics to Economics


Credit hours

In-class work
per week
Practice
per week
Credits
Duration
Total
6
2
8
10 weeks
120 hours

Instructor
Adriano Júlio de Barros Vicente de Azevedo Filho
Ana Lucia Kassouf

Objective
The course is intended to provide basic concepts and theoretical foundations of probability and statistics
in order to prepare for disciplines and research in the areas of Econometrics, Economics of Uncertainty,
Game Theory, Decision and Risk Analysis, Simulation, Stochastic Processes and Probabilistic Modeling in
general. The main objectives of the course include training the student in understanding, modeling and
solving problems involving probabilities and statistical inference, aiming to improve their capacity for
analysis and abstraction in situations involving uncertainty.

Content
1. Deductive Inference x Inductive Inference: Basic concepts of formal logic, syllogisms, inductive
reasoning. Causality and logical implication. Alternative notions of statistics (classical and Bayesian
view). Understanding the meaning of axioms, theorems, lemmas, propositions, corollaries. Superficial
notions about the main methods used in proofs of theorems. 2. Algebra of Events and Probability
Axioms: Experiments, events, algebra of sets and events. Axioms of probability / conditional probability.
Bayes theorem. Discrete and continuous spaces. Probability trees. Notions of combinatorial analysis. 3.
Random Variables, Probability Distributions and Moments. Basics for discrete case and continuous case.
Density and distribution function (cumulative). General properties of distributions. Moment-generating
functions. Mathematical hope, variance, moments, measures of central tendency. Properties of hope and
variance. Multivariate distributions. Covariance. Conditional and marginal distributions. Conditional Hope
and Variance. Moment-generating functions and characteristic function. Regression. Independence.
Markov, Chebyshev and Jensen inequalities. 4. Modes of Convergence of Laws of Statistics: Law of Large
Numbers and Central Limit Theorem. 5. Parametric Probability Distributions. Notions and properties of
discrete (Bernoulli, Binomial, Poisson, Negative Binomial and others.) and continuous (Normal, Uniform,
Exponential, Log-Normal, Gamma, t-student, F, Chi-Square and others) distributions commonly used.
Approximations and mixtures of distributions. 6. Distributions of Random Variable Functions. Expectation
and variance. Approaches. Cumulative function technique, maximum and minimum distributions.
Technique of the moment generating function. Technique of transforming and changing variables.
Probability integral transformation theorem. Distributions of Functions of Random Variables by Monte
Carlo Simulation. Transformations in multivariate and Jacobian cases. 7. Estimates for Points.
Understanding estimators and statistics. Properties of estimators. Measures. Strategies for choosing
estimators. Least squares method. Method of moments. Bayesian Estimators. Estimation by maximum
likelihood: properties, Cramer-Rao limit, consistency, invariance, normality by convergence. 8.
Estimates for Intervals. Confidence intervals. Unilateral and bilateral intervals. Results for normal
samples, ranges for hope and variance. Bayesian ranges. 9. Testing and Hypothesis Selection. Basic
concepts. Types and dimensions of errors. Limitations. Decision theory and statistical tests Bayesian
notions. 10. Introduction to Econometric Regression Models. Basic principles. Least Squares Method.
Elementary Tests.

Bibliography
Amemiya, T. 1994. Introduction to Statistics and Econometrics. Harvard University Press, Cambridge.
Azevedo-Filho, A. 2010. Principios de Inferência Dedutiva e Indutiva: Noções de Lógica e Métodos de
Prova. CreateSpace (EUA). Azevedo-Filho, A. 2011. Introdução à Estatística Matemática Aplicada - Vol I:
Fundamentos. CreateSpace (EUA). Azevedo-Filho, A. 2011. Introdução à Estatistica Matemática Aplicada
- Vol II: Distribuições Paramétricas e Simulação. CreateSpace (EUA). Azevedo-Filho, A. 2007.
Probabilidades III - Distribuições Paramétricas Discretas e Contínuas. USP/DEAS - Série Didática, No. D-
133, 150p, Berger, J. 1993. Statistical Decision Theory and Decision Analysis, 2nd Edition, Springer,
617p, Berger, J. 2003. Could Fisher, Jeffreys and Neyman have agreed on testing? Statistical Science,
18:1-32, 2003 Berndt, E. 1996. The Practice of Econometrics: Classic and Contemporary. Addison-
Wesley, 702p. DeGroot, M. 1986. Probability and Statistics. Addison-Wesley. Drake, A. 1967.
Fundamentals of Applied Probabilistic Analysis. McGraw-Hill, New York. Greene, W. H. 2007.
Econometric Analysis. 6th Edition, Prentice Hall, Englewood Cliffs. Hoffmann, R. 2006. Estatística para
Economistas. 4ª. Edição, Editora Thomson Learning, São Paulo. Hoffmann, R. e Vieira, S. 1977. Análise
de Regressão: uma Introdução à Econometria. Hucitec-Edusp Hubbard, R. e Amstrong, J. 2006. Why we
don't really know what statistical significance means: Implications for educators. Journal of Marketing
Education, Volume 28, no. 2, 2006, Pages 114-120. Intriligator, Bodkin e Hsiao 1996. Econometric
Models, Techniques and Applications. 2nd Edition, Prentice-Hall. Mood, A., Graybill, F. A and Boes, D.
1989. Introduction to the Theory of Statistics. McGraw-Hill, New York. O'Haggan, A. e Luce, B. 2003. A
Primer on Bayesian Statistics. Centre for Bayesian Statistics in Health Economics, MEDTAP International,
2003. Spanos 1999. Statistical Foundations for Econometric Modelling with Observational Data.
Cambridge University Press.