Exploring Cumulative Incomefunctions by Functional Data Analysis

Abstract: Cumulative incomes can be seen as the added yearly incomes for some distinct amount of years. It can also be thought of as a continuous curve, where income continuously flows into ones account. The analyzing of curves, or functions, instead of uni- or multivariate data, needs and enables different approaches. In this thesis, methods called Functional Data Analysis are used to show how analyzes of such cumulative income curves can be done, mainly through functional adaptions of principal component analysis and linear regression. Results shows how the smoothing of curves helps to decrease variances in a bias-variance trade-off, while having problems accounting for data containing many low valued observations. Furthermore, results indicates that education might have an effect, when controlling for employment rate, in the sample.