In this project we consider the problem of building a quantile regression model to analyze risks in medical malpractice contest when the right predictors explaining the phenomenon have to be selected. As well known, quantile regression is an important method for implementing the impact of regressors on the whole conditional distribution of a response variable in particular on its tails. For this reason quantile regression is particular attractive when risk assessment is the main concern i.e. when the events are extreme. How to select the best predictors and estimate the right parameters in model building is critically important and here we will consider the penalized regression approach propose by Tibishirani in 1996 focusing the attention on the lasso and the elastic net framework. We will use those tools in the quantile regression contest building specific algorithms to implement the frequentist and the Bayesian statistical inference. Once the methodological part is implemented, we will use those tools in the medical malpractice risk assessment which is particular important for the risk managers of health care institutions involved in measuring frequencies, claims intensities of damages and amount of costs for them. Since several variables are involved in explain those phenomena it seems quite interesting to choose the right ones by using a penalizing quantile regression approach. This would be, to the best of our knowledge, the first quantile regression approach to face the medical malpractice issue.
