Non-parametric statistical models using wavelets: Theory and methods

Abstract

Machine Learning and Data Analytics have become key tools in the advancement of modern society, with a vast variety of applications exhibiting exponential growth in breadth and depth during the past few years. Moreover, the advancement of data-gathering technologies enables the availability of massive amounts of data, which fuels the opportunity for application and development of new analytics tools to obtain insights, making an effective and efficient use of it. This dissertation aims to contribute to the scientific existing methodologies in this context, with focus in the non-parametric statistical domain due to its robustness to prior modeling assumptions and flexibility of application in many different contexts. In light of this objective, four non-parametric methodologies based on wavelets are introduced and analyzed. Problems such as survival density estimation, non-linear additive regression and multiscale correlation analysis are covered, and each methodology is studied from both a theoretical and pragmatic perspectives. Moreover, a theoretical foundation for each proposed method is developed, and then its applicability and performance are illustrated using simulations studies, real data sets and comparison with previously published results in the field.