Statistical methods are crucial to understand reality and foster progress of scientific knowledge, providing rigorous models and methods to analyse data and come up with correct conclusions. In practice, a huge number of research questions are posed from different fields such as, health studies, epidemiology, biology, environmental and social sciences. In all these fields, the data exhibit complex patterns that require sophisticated statistical tools for their analysis. Therefore, the mathematical statistician is in front of a variety of challenges. The first one is to propose a model together with a statistical method that may properly solve the given problem. Secondly, the theoretical properties of the proposed method must be studied to identify the situations in which it will lead to consistent answers. Particular cases are then to be explored by simulation studies, where the method performance is investigated in real life scenarios. Third, code or friendly-use software should be packaged to help the practitioner in the application of the method to a specific data set. Finally, the collaboration with researchers in other areas in order to provide statistical expertise in the application of the methods is also a goal. This project aims to cover all these edges of statistical research.