Least Squares Regressions with the Bootstrap:A Survey of their Performance

Diploma Thesis from the year 2009 in the subject Mathematics - Statistics, grade: 1,6, University of Bonn (Statistische Abteilung der Rechts- und Staatswissenschaftlichen Fakultنt), course: Diplomarbeit bei Prof.Dr. Alois Kneip, language: English, abstract: The statistical technique called bootstrap is usable with a lot of inferential problems and it is the main topic of this paper. Since the bootstrap provides material for a whole series of books it is essential to pick one special aspect of the bootstrap and investigate it in depth, otherwise the analysis would inevitably become too general. This aspect is the topic of regression. Hence, this paper will introduce the bootstrap and compare the performance of the new inference methods which it provides with some classical methods of judging a regression which were used in the years before the bootstrap. Therefore the remainder of this paper is as follows: First there will be a description of the basic model in which all of the following investigations will be done, chapter two. The next chapter will describe the different regression techniques which try to solve the model. The fourth chapter is going to show the behavior of these regression techniques in large samples, i.e. shows some classical methods of statistical inference. Following chapter five will give an introduction to the bootstrap which will be succeeded by a description of the bootstrap in regression problems, chapter six. The seventh chapter will show how inference is done with the help of the bootstrap. The eighth chapter is going to compare the performances of classical and bootstrap inference in regressions. Before the concluding remarks of chapter ten, there will be a practical application in chapter nine which tries to prove some observations of the preceeding chapters.