Statistical Modelling 6 (2006), 279299
Comparing nonparametric surfaces
Adrian W. Bowman
Department of Statistics
The University of Glasgow
Glasgow G12 8QQ
UK
eMail:
adrian@stats.gla.ac.uk
Abstract:
There is a wide variety of problems where the object of primary interest
is a surface. Environmental studies in particular, where data often have
a spatial structure, provide many examples where estimation of a surface
is a central component of analysis. In these settings, the surfaces are
often not well described by simple parametric models. Nonparametric
regression therefore offers a convenient means of constructing surface
estimates in a straightforward manner. In this paper, the issues
associated with comparing such regression surfaces across different
groups of data are discussed. Formal methods for assessing the equality
of a collection of surfaces, or the suitability of a set of parallel
surfaces, are described. These not only extend existing methods of
nonparametric analysis of covariance but also allow the commonly occurring
case of correlated errors to be incorporated. Graphical methods to provide
insight into the sources of departure from a candidate model are also
proposed. Several applications are provided to illustrate and explore
the proposals.
Keywords:
analysis of covariance; graphical methods; local linear methods;
nonparametric regression; quadratic forms; smoothing spatial data;
surface estimation
Downloads:
Data
and software in zipped archive
back