Syllabus (detailed contents):
• Review of the definitions and properties of the usual distributions (normal, Chi-square, Student’s, Fisher’s, Gaussian vectors, etc.) and probabilistic tools (law of large numbers, central limit theorem, Slutsky’s lemma)
• Estimation in a parametric model: method of moments, maximum likelihood
• Cramer-Rao bound, and efficiency of an estimator
• Confidence interval for the mean and the variance of a Gaussian or a non-Gaussian sample
• Parametric hypothesis testing: concept, tests on the mean and the variance of a Gaussian sample, tests on a proportion, p-value, test for comparing two independent Gaussian samples, Neyman-Pearson’s lemma, maximum likelihood ratio tests