Applications deadline April 30th
Intermediate knowledge of econometrics
Course outline, objectives and learning outcomes
Recent years have seen a massive increase in the availability of large data sets. In this course we will cover some of the techniques that have been developed to analyze such data sets. Particular attention will be given to precise estimation, variable selection, and hypothesis testing. We will also see how to implement the some of the techniques in R.
1. The Lasso and some of its asymptotic properties when the dimension of the model is fixed.
2. Introduction to the oracle property. The adaptive Lasso as an example of an estimator possessing the oracle property.
3. The adaptive Lasso for instrumental variable selection.
4. The adaptive elastic net for generalized method of moments.
5. Upper bounds on the estimation error in the `∞-norm and variable selection via thresholding.
6. Finite sample oracle inequalities for the Lasso when the number of variables is larger than the sample size.
7. Oracle inequalities and inference in high-dimensional VAR models. Some results from applications to large macroeconomic data sets.
8. Uniformly valid inference in high-dimensional models when the number of variables is larger than the number of parameters.
9. How to use the glmnet and the lars package in R to implement Lasso-type estimators.
References and textbooks for the course:
P J Bickel, Y Ritov, and A B Tsybakov. Simultaneous analysis of lasso and dantzig selector. The Annals of Statistics, pp 1705–1732, 2009.
P Bühlmann and S Van De Geer. Statistics for high-dimensional data: methods, theory and applications. Springer Science & Business Media, 2011.
L A F Callot and A B Kock. Oracle efficient estimation and forecasting with the adaptive lasso and the adaptive group lasso in vector autoregressions. Essays in Nonlinear Time Series Econometrics, pp 238, 2014.
M Caner and Q Fan. Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso. Journal of Econometrics, 187(1):256–274, 2015.
M Caner and A B Kock. Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative lasso. arXiv preprint arXiv:1410.4208, 2014.
M Caner and H H Zhang. Adaptive elastic net for generalized methods of moments. Journal of Business & Economic Statistics, 32, pp 30– 47, 2014.
K Knight and W Fu. Asymptotics for lasso-type estimators. Annals of Statistics, pp 1356–1378, 2000.
A B Kock and L Callot. Oracle inequalities for high dimensional vector autoregressions. Journal of Econometrics, 186, pp 325–344, 2015.
K Lounici. Sup-norm convergence rate and sign concentration property of lasso and dantzig estimators. Electronic Journal of Statistics, 2, pp 90–102, 2008.
S van de Geer, P Bühlmann, Y Ritov, and R Dezeure. On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics, 42, pp 1166–1202, 2014.
S van de Geer. Estimation and testing under sparsity. Springer, 2016.
H Zou. The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101, pp 1418–1429, 2006
Participants will use their laptops with R already installed on them.
The Module will be held in the Bank of Italy's Scuola di Automazione per Dirigenti Bancari (SADiBa), via San Marco n.54, Perugia. Participants will be accommodated at SADiBa.
Fees and Enrollment
- Students and university staff: 800€
- Others: 2300€
Fee includes: Fee includes full board accommodation starting from Sunday.