de Uña-Álvarez, Jacobo; Pardo Fernández, Juan Carlos
Statistics is a fundamental piece in the progress of scientific knowledge, as it provides rigorous models and methods to analyse data and come to correct conclusions. The applications of the statistical procedures appear in almost any branch of knowledge: medicine, biology, engineering, economy, social sciences, etc. Nowadays, data are becoming more and more accesible, but also demand more sophisticated methods to be analysed. The role of a researcher in mathematical statistics consists of several scientific activities. First of all, the researcher develops new models and methods to deal with new problems, or alternative methods for existing ones. The rigorous mathematical treatment of these models and methods, the study of their theoretical properties and the analysis of their practical performance in simulation studies and in applications occupy a main part of our research activity. Second, the computational implementation of the methods and its dissemination amongst the scientific community is also done by the statistical researcher. Finally, the collaboration with researchers in other areas in order to provide statistical expertise in the application of the methods is also our duty. This project covers the three abovementioned aspects: development and study of new statistical models and methods, practical implementation and application to other areas. Statistical models range over a large set of possibilities, from very simple to extremely complicated. Normally, a compromise between several aspects such as simplicity, interpretability and flexibility is desirable. In this regard, nonparametric and semiparametric statistics are well positioned, as they are flexible enough and can reach good results in a large variety of situations without imposing unrealistic hypotheses to the models. Unlike, parametric statistics, where the objective is to estimate finite-dimensional parameters, the objective of nonparametric statistics is to estimate and perform inference about curves. Here, the term "curve" must be understood in a broad sense and includes density functions,cumulative distribution functions, regression functions, variograms, etc. This project focuses on the development of new models and methods in nonparametric and semiparametric statistics. Curve estimation and inference, specially testing procedures, form the core of the project. The rigorous analysis of the proposed methodologies, their practical implementation and their application are the cornerstones of this proposal. More specifically, this project contributes with new advances in methods for high-dimensional data, survival analysis, nonparametric regression, ROC curves, goodness-of-fit testing and testing hypotheses in regression models. Besides, applications to other areas and the elaboration of friendly-use code in R are also intended. This project will contribute in a deeper knowledge of methods in nonparametric and semiparametric statistics. The expected outcome is twofold: publications in specialized highstandard journals in the area of statistics and collaborations with researchers in other areas. The project is the natural continuation of four previously funded projects (MTM 2005, 2008, 2011 and 2014).