Abstract

Functional data refer to data which are in the form of functions or smooth curves that are assessed at a finite, but large subset of some interval. In this thesis, we explore methods of functional data analysis, especially curve registration, in the context of climate changes in a group of 16 cities of the United States. In the first step, spline functions were developed in order to convert the raw data into functional objects. Data are available in function forms, but the mean function which was obtained by the unregistered curve fails to produce a satisfactory estimator. This means that the mean function does not resemble any of the observed curves. A significant problem with most functional data analyses is that of misaligned curves.
Curve registration is one method in functional data analysis that attempts to solve this problem. In the second step, we used curve registration method based on "landmarks alignment" and "continuous monotone registration" in order to construct a precise measurement of the average temperature. The results show the differences between unregistered data and registered data and a significant rise of the temperature in U.S. cities within the last few decades.