1 ) Preliminary results and advanced inferential notions: Orthogonal projections and linear equations, mean vectors and covariance matrices, moments generating functions , normal vectors, linear transformations and independence. Centered estimation , sufficient and complete statistics ; Theorems Rao- Blackwell and Blackwell- Lehman - Scheffé; Cramer - Rao Inequality , efficient estimators , estimable vectors ;
2 ) Advanced inferential notions: Techniques for point estimation , confidence intervals and hypothesis testing , including the study of the power of tests using resampling techniques; study of distributions associated with normal; numerical methods leading to optimization tasks of calculatiions - the QR method of Francis and method SVD ( Singular – Value Decomposition ) - stressing its relevance in the identification of parameters and models; statistical model selection:, Akaike ( AIC ) , Bayesian information criterion ( BIC), maximum likelihood ratio test; quality assessment of models - bootstrap and cross-validation .
3 ) Analysis of assumptions and development of multilinear regressions : Study tof the standard case of multilinear regression - adjustment and normality ; Gauss - Markov theorem ; multilinear regressions with exact linear restrictions .
4 ) Simultaneous linear equations and structural equations based on partial covariance structures and minimum parcial squares . The interaction in structural equation models.