Advanced Topics in Statistical Inference
Code
9705
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Isabel Cristina Maciel Natário
Total hours
56
Teaching language
Português
Objectives
In this course we want to give students a solid formation in the areas of Fundamentals of Statistics, Estimation, Inference, Linear Regression and Analysis of Variance Models and a brief introduction to Bayesian Statistics. It is this way intended that the students may acquire the ability to fully understand the essence of these subjects in such a way that they will be able to apply them in a variety of situations.
Prerequisites
Knowledge of Probability and Statistics at the level of those obtained at the courses Probability and -statistics I and II of the undergraduate degree in Mathematics.
Subject matter
- Preliminaries: noint moment generating functions and characteristic functions; mean vectors and covariance matrices; linear transformations and reproducibility; orthogonal partitions; unbiased estimation: sufficient and complete statistics.
- Convergence in distribution, in probability and with probability 1 of random vectors.
- Centered estimation: Rao-Blackwell and Blackwell-Lehman-Scheffé theorems and Cramer-Rao lower bound for random vectors; Efficiency; estimable vectors.
- Orthogonal models; Mixed orthgonal models: algebraic structure; variance components; segregated models; inference.
- Mixed Non-orthogonal models: Triple minimization; inference; variance components; estimable vectors.
Bibliography
Casella G e Berger RL (2002). Statistical Inference - 2nd edition. Duxbury Press.
Paulino CD, Amaral-Turkman MA, Murteira B (2003). Estatística Bayesiana. Fundação Calouste Gulbenkian.
Mood, Graybill e Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
Rohatgi VK, Saleh AK (2001). An Introduction to Probability Theory and Mathematical Statistics. Wiley & Sons.
Box GEP, Tiao GC (1973). Bayesian Inference in Statistical Analysis. Wiley-Interscience.
DeGroot MH (1989). Probability and Statistics - 2nd edition. Addison-Wesley.
Paulino CD (2000). Notas de Inferência Estatística. Associação de Estudantes do IST.
Teaching method
Classes/Labs exposed in slides with proposals of resolutions of problems, debated in Moodle discussion foruns and also via skype. Moddle page with progressive inclusion of the work being done.
Evaluation method
4 sets of proposed problems, with a weight of 25% for the final grade each.