Quantitative Methods and Statistical Learning

The indicative module outline is as follows:

Foundations of Statistical Inference: Descriptive statistics, probability distributions and sampling theory, point estimation, confidence intervals and hypothesis testing.

Regression I: Simple and multiple linear regression model, goodness of fit, hypothesis testing on individual coefficients and joint significance, interpretation and application on case studies with R.

Regression II: Dummy variables and interaction terms, units of measurement and estimated coefficients, logarithmic and polynomial models, overview of Instrumental Variables (IV) regression, interpretation and application on case studies with R.

Time Series Analysis I: Properties of time series data, autocorrelation and partial autocorrelation functions (ACF/PACF), autoregressive process (AR), deriving the autocorrelation function of an AR(1) process, interpretation and application on case studies with R.

Time Series Analysis II: The moving average process (MA), deriving the autocorrelation function of an MA(1) process, stationarity, the Augmented Dickey Fuller (ADF) test, the ARIMA(p, d, q) model, the BoX-Jenkins methodology for model selection, interpretation and application on case studies with R.

Panel Data Analysis I: Structure of panel data, pooled OLS and the fixed effects estimator (within transformation), unit and time fixed effects, interpretation and application on case studies with R.

Panel Data Analysis II: Random effects estimator, fixed vs random effects with the Hausman test, clustered standard errors, endogeneity, overview of dynamic panels, interpretation and application on case studies with R.

Binary Choice Models I: The linear probability model (LPM) and its limitations, the logistic function and its link to utility theory, the logit regression, odds ratios and marginal effects, interpretation and application on case studies with R.

Binary Choice Models II: The multinomial regression model, ordered choices and ordered logit, interpretation and application on case studies with R.

Contemporary Approaches: An overview of resampling methods (the bootstrap, cross validation, jackknife), an introduction to quantile regression, shrinkage methods (lasso and ridge regression) .

Supervised and Unsupervised Learning: Principal Component Analysis (PCA), eigenvalue decomposition and scree plots, selection of components, factor analysis vs PCA, the role of PCA in constructing composite indicators, the PCA regression, an overview of Partial Least Squares Regression, an overview of Multiple Correspondence Analysis (MCA) and its statistical foundation, the Principal Components Pursuit (PCP) algorithm.