Statistical Inference I
(i) Concepts of sample, unknown population parameters and statistics. (ii) Introduction to point estimation theory. (iii) Optimality criteria: Mean Squared Error, unbiasedness. (iv) Information Inequality, Cramér-Rao variance lower bound and Fisher information. (v) Sufficient statistics and completeness, Uniformly Minimum Variance Unbiased Estimators (UMVUE). (vi) Estimation in an exponential family of distributions. (vii) Basu’s Theorem, independence of the sample mean and the sample variance in a normal population. (viii) Sampling distributions (X2, t, F). (ix) Point Estimation procedures: Maximum Likelihood Estimation (MLE), the method of moments. (x) Statistical decision procedures, Bayes and Minimax estimators. (xi)Confidence Interval Estimation.
In order to highlight the special educational and didactical aspects of a course, special emphasis is given on the historical evolution and scientific development of the subject as well as on its applications in technology and/or other sciences.