Mathematical Statistics Topics

Mathematical Statistics Topics

Cod: 23037

Department: DCET

Department: DCET

ECTS: 10

Scientific area: Statistics

Scientific area: Statistics

Total working hours: 260

Total contact time: 10

Total contact time: 10

This learning unit aims to provide advanced knowledge and develop deep skills in statistical modeling and inference. It addresses three main components: the study of preliminary results and inferential notions; the development and analysis of multilinear regressions; and the study of simultaneous linear equations and structural equations.

Multilinear regressions

Simultaneous linear equations

Structural equations

Simultaneous linear equations

Structural equations

- Know the concepts and inferential methods and to perform applications with the support of statistical software;

- Develop and apply multilinear regressions, namely to real datasets with computer support, identifying and interpreting optimal solutions for decision support;

- be familiar with the types of simultaneous linear equations and structural equations;

- Investigate new methodologies, as well as make improvements to the existing ones.

- Explore applications of these methodologies by using real datasets and taking advantage of computer support, developing and using appropriate software.

- Develop and apply multilinear regressions, namely to real datasets with computer support, identifying and interpreting optimal solutions for decision support;

- be familiar with the types of simultaneous linear equations and structural equations;

- Investigate new methodologies, as well as make improvements to the existing ones.

- Explore applications of these methodologies by using real datasets and taking advantage of computer support, developing and using appropriate software.

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.

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.

- Hoyle, R.H. (2012). Handbook of Structural Equation Modeling. The Guilford Press.

- Rao, C. R. & Turtenburg, H. (1998) Linear Models: Least Squares and Alternatives 2nd ed Springer.

- Muller, K. E & Stevent, K. E. (2006) Linear Theory: Univariate, Multivariate and Mixed Models John Willey & Sons.

- Rao, C. R. & Turtenburg, H. (1998) Linear Models: Least Squares and Alternatives 2nd ed Springer.

- Muller, K. E & Stevent, K. E. (2006) Linear Theory: Univariate, Multivariate and Mixed Models John Willey & Sons.

E-learning

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.

This Learning Unit will not be open in 2015/16.