Een studie en implementatie van robuuste schatters voor multivariate en functionele gegevens

Beran (2003) defined statistics as the study of algorithms for data analysis. In many situations several variables need to be taken into account simultaneously to accurately describe the patterns in the data. In practice this is done by fitting a model to the data. Often, real life data sets also contain outliers, i.e. observations inconsistent with the multivariate patterns of the majority of the data. Outliers tend to exert a disproportionate pull on the fit thereby blurring the main patterns in the data as well as their true outlyingness. Robust estimators are designed to prevents arbitrarily outliers from exerting undue influence on the fitted model. Several approaches to obtain robust estimates exist depending on the characteristics of the data. In Chapter two we compare many robust estimators of multivariate location and scatter by means of simulations. An important conclusion of this chapter is that in many situations those algorithms do not always reveal the outliers (or prevent them from swaying the fit). A fundamental problem in statistics is that of estimating the linear relationship between multiple design variables and a single response variable. Though many robust algorithms have been developed to fit such (so-called regression) models, sometimes, in applications, they suffer from being too slow and/or random. In Chapter 3, we propose a new robust algorithm for regression that is both quick and deterministic. Functional data can be seen as structured multivariate data collected from an underlying collection of smooth processes, or "curves". Often, the interest will be on estimating the main features of these curves such as their central tendency or variability as well as identifying sub-groups of curves detached from the majority. Chapter 4 offers an new approach to do this and compares it with state of the art alternatives by means of simulations. The general availability of open source, portable, versatile and easy to use software libraries written in an up to date programing paradigm is an important component in the success of procedures in computational statistics. A library of algorithms for depth and related data analytical tool has been developed as part of the work that led to this thesis. Chapter 5 show cases many components of this library and discuss how these improve upon available alternatives.nrpages: 148status: publishe