Graduate Program

__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

Idemauro Antonio Rodrigues de Lara

Renata Alcarde Sermarini

__Objective__

Each the methods most commonly used for estimation of parameters, confidence intervals and hypothesis testing.

__Content__

1. Review topics: uni and multidimensional random variables. Conditional Distributions.

Transformations of random variables. Mathematical hope, variance, covariance, hope and

conditional variance. 2. Characteristic function and properties. 3. Inequalities and Identities

probabilistic. 4. Random variable sequence conversions: in probability, almost certain,

in average r and in distribution. Strong law and weak law of large numbers. Central Limit Theorem.

Delta uni and multivariate method. 5. Maximum Likelihood Theory: Estimation and Properties

asymptotic estimates. Lower limit of Cramér-Rao quota. 6. Hypothesis Tests:

substantiation, more powerful tests, Neyman-Pearson's motto, likelihood ratio test,

Wald test and Score test. Wilk's theorem. 7. Approximate random intervals and regions of

confidence. 8. Special topics of inferences centered on maximum likelihood theory.

__Bibliography__

Bickel, P.J. e Doksum, K.A. Mahematical Statistics: basic ideas and selecetd topics. 2nd ed, Prentice Hall, 2001.

Bickel, Casela, Livro de Probabilidades do IME-USP

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.

James, B.R. Probabilidade: um curso em nível Intermediário. Projeto Euclides, Rio de Janeiro, 2008.

Kendall, M.G. e Stuart, A. The Advanced Theory of Statistics. Vol I, II, III. Charles Griffin, London, 1963.

Lindegren, B.W. Statistical Theory. McGraw-Hill, 1974.

Murteira, B.J.F. Probabilidade e Estatística, Vol I e 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.