INFERENTIAL STATISTICS

Samples and sampling distributions. Convergences of sequences of random variables. Law of large numbers. Central limit theorem and its applications. Monte Carlo approximations. Sampling from the Normal distribution. Statistical models. Bernoulli model, location Normal model, location-scale Normal model. Likelihood function. Sufficient statistics. Maximum likelihood estimates. Mean squared error. Bias, standard error, consistency. Confidence intervals. Confidence intervals in the Bernoulli model, the location Normal model, the location-scale Normal model. Testing hypotheses. P-values, statistical significance, practical significance, critical values. One-sided and two-sided tests. Hypothesis assessment via confidence intervals. Testing hypotheses in the Bernoulli model, the location Normal model, the location-scale Normal model. Sample size determination. Inference on a variance. Distribution-free (non parametric) methods. Method of moments. Bootstrap method. Inference about quantiles. Least squares method. Ordinary least squares estimates in the simple linear regression model. ANOVA decomposition in the simple linear regression model. Hypotheses testing about the parameters of the simple linear model.

ECONOMETRICS

The simple regression model. Multiple regression analysis: estimation. Multiple regression analysis: inference. Multiple regression analysis: OLS asymptotics. Multiple regression analysis: further issues. Multiple regression analysis with qualitative information. Heteroskedasticity. More on specification and data problems. Basic regression analysis with time series data. Panel data. Instrumental variables estimation. Simultaneous equations models. Limited dependent variable models. Advanced time series topics.