The course examines further notions in the context of statistical estimation and hypothesis testing. We investigate the following: 1. Probability spaces, probability distributions, random variables and distributions on R, representation by cumulative and density functions, moments and moment generating functions, probability distributions on Euclidean spaces, homogeneity and independence. 2. Statistical model, parameterization, specification and identification. Estimators and properties, Neyman-Pearson theory of hypothesis testing, structure of hypotheses, errors, test statistics and decision, power functions and comparisons between tests. 3. Parametric models and likelihood function, maximum likelihood estimator, Cramer-Rao bound, likelihood ratio test and the Neyman-Pearson lemma.
Indicative Course Prerequisites: Statistics Ι