Date of Award

May 2016

Degree Type

Thesis

Degree Name

Master of Science

Department

Mathematics

First Advisor

Daniel Gervini

Committee Members

Wei Wei, Peter Hinow

Abstract

There is the saying which says you cannot see the woods for the trees. This

thesis aims to circumvent this unfortunate situation: Longitudinal data on

tree growth, as an example of multiple observations of similar individuals

pooled together in one data set, are modeled simultaneously rather than

each individual separately. This is done under the assumption that one

model is suitable for all individuals but its parameters vary following un-

known nonparametric random effect distributions. The goal is a maximum

likelihood estimation of these distributions considering all provided data and

using basis-spline-approximations for the densities of each distribution func-

tion over the same spline-base. The implementation of all procedures is

carried out in R and attached to this thesis.

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