On nonparametric and neural networks techniques for regression

Abstract

The context of this Thesis lies in the field of Econometrics. Our objective is to analyze various Nonparametric and Neural Networks techniques for regression. The first chapter of the Thesis is preoccupied with the analysis of the kernel density estimator, which is a fundamental step towards using kernel functions in regression. The second chapter is preoccupied with regression analysis by means of local polynomials. We will explore the techniques, their properties and their limitations. The third chapter is preoccupied with neural networks analysis. Specifically we present the structure of a one-hidden-layer and a two-hidden-layer feed forward neural network and explore their applications in regression. In the appendix we provide proofs for all the results that need to be validated throughout the thesis, namely, asymptotic (un)biasedness, consistency and asymptotic normality of the proposed estimators and the universal approximation theorem for neural networks in both the unit cube and the n-dimensional real space. We have used the R programming language for our analysis. We provide the algorithms in the appendix.