Given the importance that it takes the teachings of the various sub-disciplines oriented as 'quantitative methods' (theoretical econometrics, applied econometrics, financial econometrics etc.), and on the other hand the heterogeneity of the students in this master, this course wants to be a global revision of concepts introduced (maybe) in a basic way during the license (L2 L3). At the same time the thorough study of the various probabilistic and statistical techniques necessary to practice or understand these concepts in other subjects taught in the Master (M1 or M2).
Course overview :
1 Revision real univariate random variables. Probability distribution induced by a r.v. 2 Functions associated to a r.v. and their properties (density and distribution functions). 3 Main families of continuous and discrete r.v. used in statistics and econometrics. 4 Theoretical and empirical Moments. Statistical properties. Skewness. Kurtosis. 5 Moment generating function and his properties. Computation of theoretical moments for various families. 6 Types of convergence for sequences of r.v. (in probability, almost sure, in distribution). 6 Inequalities between moments and applications - Chebyshev' inequality and the Law of Large Numbers - Cauchy-Schwarz inequality and linear correlation coefficient. 7 Families closed to the sum. Levy theorem. Central Limit Theorem. 8 Gaussian approximation to various laws. 9 Method of moments to estimate the parameters of a r.v. 10 Method of maximum likelihood. Fisher information. Cramer-Rao theorem. 11 Point estimation and confidence interval. Hypothesis testing. 12 Delta Theorem in the parametric case. Applications. 13 Weak exogeneity, strong exogeneity. Misspecification. 14 Deduction of classical nonparametric estimators and their statistical properties : - Empirical distribution function - Parzen-Rosenblat estimator for the density - Nadaraya-Watson estimator for the regression. 15 Revision and solution of a previous exam.