Credit hours
In-class work per week |
Practice per week |
Credits |
Duration |
Total |
3 |
1 |
8 |
15 weeks |
120 hours |
Instructor
Edwin Moises Marcos Ortega
Fábio Prataviera
Idemauro Antonio Rodrigues de Lara
Renata Alcarde Sermarini
Objective
Prepare doctoral students for the development of statistical methods.Apply statistical inference concepts.
Content
SUMMARY: Convergence and asymptotic theory. Statistical inference methods.
PROGRAM CONTENT: 1. Review of Probability Theory. 2. Inequalities and probabilistic identilies. 3.
Function characteristic and properties. 4. Convergences of sequences of random variables: in
probability, almost certain, in mean-r and in distribution. Strong law and weak law of large numbers.
Central Limit Theorem. Delta method. 5. The maximum likelihood theory: estimation and asymptotic
properties of the estimators. 6. Hypothesis tests: fundamentals, more powerful tests, Neyman-
Pearson's lemma, likelihood ratio test, Wald test and score test. Wilk's theorem. 7. Random approximate
intervals and regions of confidence. 8. Special topics of inferences centered on the theory of maximum
likelihood.
Bibliography
Bickel, P.J. e Doksum, K.A. Mahematical Statistics: basic ideas and selecetd topics. 2nd ed, Prentice
Hall, 2001.
Casella G.; Berger L.R. Statistical Inference. 2ª edição, Duxbury Press, California, 2002.
Cox, D.R. e Hinkley, D.V. Theoretical Statistics. Chapman-Hall, 1992.
Degroot, M.H. Probability and Statistics. Addisson-Wesley, 3rd ed, 2002.
Hoog, R.V. e Craig, A.T. Introduction to Mathematical Statistics, 3rd Edition, McMillan, 1978.
Lindegren, B.W. Statistical Theory. McGraw-Hill, 1974.
Murteira, B.J.F. Probabilidade e Estatística, Vol II, 2ª. Edição. McGraw-Hill, Portugal, 1990.
Mood, A.M.; Graybill, F.A. and Boes, D. Introduction to the Theory of Statistics. 3rd ed, McGraw-
Hill,1974.
Nikulin, M., Commenges, D. and Huber, C. Probability, Statistics and Modelling in Public Health, 1rd,
Sptinger Verlag, New York, 2005.
Przemyslae, G. Soft Methods in Probability, Statistics and Data Analysis. 1rd. Springer Verlag, New York,
2002.
Roussas, G.G. A First Course on Mathematica Statistics. Addisson-Wesley, 1973.
Silvey,S.D. Statistical Inference. Chapmann & Hall. London. 191p. 1995.