Methodology and Statistics
International Conference, 14 - 17 September 2003
FDV, Ljubljana, Slovenia


Wojtek J. Krzanowski
University of Exeter

Multivariate measurements are often made in either a spatial or a temporal context. Examples of the former occur in environmental reconnaissance programs that are carried out in many countries, where measurements are taken on a large set of different chemical elements at various locations throughout the study area. An example of the latter occurs in industrial process control, where a range of output measures is monitored on a regular basis, such as daily or weekly, across a period of time.

Principal component analysis (PCA) is often used on such data sets to identify important combinations of the original variables, either as a focus for more detailed study or to explain any significant outcomes shown up by omnibus tests. However, while PCA and related projection techniques from the standard multivariate repertoire are optimal under independence of observations and random sampling, they are not explicitly designed to address or to exploit the strong auto-correlation and cross-correlation structures that are often present in multivariate spatial or temporal data. Consequently their use may produce misleading results.

In this talk, several alternative projection techniques that are tailored to multivariate spatial and temporal data will be introduced and described. Like PCA these methods linearly transform the original variables into uncorrelated components, but instead of maximising variance these components are designed to have particular spatial or temporal properties. They can thus be viewed as optimal components to use in a spatial or temporal setting.

The technical derivation of the methods will be presented, their general performances and properties will be demonstrated via simulation results, and their specific applications will be illustrated on several real data sets. The advantages of the new methods over the more traditional ones such as PCA will be highlighted in these examples.