Sequential methods for design-adaptive estimation of discontinuities in regression curves and surfaces

Sequential Methods for Design-adaptive Estimation of Discontinuities in Regression Curves and Surfaces1 by Peter Hall

In fault-line estimation in spatial problems it is sometimes possible to choose design points sequentially, by working one’s way gradually through the “response plane,” rather than distributing design points across the plane prior to conducting statistical analysis. For example, when estimating a change line in the concentration of resources on or under the sea bed, individual measurements can ...

Adaptive sequential design for regression on multi-resolution bases

This work investigates the problem of construction of designs for estimation and discrimination between competing linear models. In our framework, the unknown signal is observed with the addition of a noise and only a few evaluations of the noisy signal are available. The model selection is performed in a multi-resolution setting. In this setting, the locations of discrete sequential D and A de...

Adaptive Subdivision Curves and Surfaces

Well-known schemes of subdivision curves and surfaces are modified so that they allow an adaptive refinement. Adaptation is controlled by an error measure which indicates for the vertices of a mesh whether the approximation is sufficient. The adaptive constructions are based on local operations of refining or coarsening. They allow to reach all other subdivisions, in particular the non-adaptive...

Approximation Methods for Algebraic Curves and Surfaces

Identifying Discontinuities in Trend Surfaces Using Bilateral Kernel Regression

Following a brief review of the kernel regression approach to estimating surface models of the form z = f(x,y) + e, this article will consider the situation where f is not a continuous surface function, and in particular where the discontinuities take the form of one-dimensional breaks in the surface, and are not specified a priori. This form of model is particularly useful when visualizing som...