Principal Investigator

P G Hall Mathematics Research Section, MSI, ANU

Project Title

Curve Estimation

Brief Description for General Publications

In many instances in applications, spatial data may be viewed as observations on an underlying regression surface. Estimation of jump curves or "fault lines" in such surfaces is then a task of primary interest. These curves may not necessarily be connected, and are allowed to split into several parts. The developed methodology for estimating fault lines caters for features which are desirable both in theory and practice, such as irregularly-spaced design. An intuitively appealing but computationally demanding approach is taken, and asymptotically (as sample size tends to infinity) confidence envelopes for this estimator were derived theoretically. This approach consists of transforming the raw data into a smooth surface wherein the fault line appears as a ridge, which is defined to be its estimator.