Tópicos Avançados de Estatística (1 º Sem 2019/2020)

Probabiity: review of basic concepts and results; convergence of sequences of random variables; convergence in distribution, in probability, in mean of order r, almost sure convergence; law of large numbers, central limite theorem, delta method.

Statistics: classical statistical model, statistics and their sampling distribution, Fisher information. Suficiency, minimal suficiency, ancilarity, completeness, exponencial family of distributions.

Estimation: unbiased estimators, Frechet-Cramer-Rao limit. Minimum variance unbiased estimation. Methods of estimation and their properties: maximum likelihood and moments estimators. Interval estimation.

Bayesian statistics: Bayes theorem as an inferential tool, the Bayesian methodology, non-informative priors, point and interval Bayesian estimation, Bayesian prediction.