Graphics Reference
In-Depth Information
and Truong (
) describe how nonparametric regression can accommodate cen-
soreddata. DiblasiandBowman(
)usesmoothing toexploretheshapeofanem-
piricalvariogramconstructedfromspatialdata,examininginparticulartheevidence
forthepresenceofspatial correlation. Simonoff(
)discussesthesmoothing ofor-
deredcategorical data, while Härdle et al.(
)describe single index modelswhich
aim to condense the information in several potential explanatory variables into an
index which can then be related to the response variable, possibly in a nonparamet-
ric manner. Cook and Weisberg (
) address the general issue of identifying and
exploring the structureofregression data, with particular emphasis onthe very help-
ful roles of smoothing and graphics in doing so. hese references indicate the very
wide variety of ways in which smoothing techniques can be used to great effect to
highlight the patterns in a wide variety of data types, with appropriate visualization
forming a central part of the process.
Sotware to implement smoothing techniques is widely available and many stan-
dard statistical packages offer facilities for nonparametric regression in some form.
he examples and illustrations in this chapter have all been implemented in the
R
statistical computing environment (R Development Core Team,
) which offers
a very extensive set of tools for nonparametric modelling of all types. he one- and
two-covariate models of this chapter were fitted with the
sm
(Bowman and Azzalini,
) package associated with the monograph of Bowman and Azzalini (
). he
mgcv
(Wood,
) and
gam
(Hastie,
) packages provide tools for generalised
additive models which can deal with a much wider distributional family beyond the
simple illustrations of this chapter.
he website associated with this handbook provides
R
sotware which will allow
the reader to reproduce the examples of the chapter and, by doing so, offers encour-
agement for the reader to investigate the potential benefits of nonparametric regres-
sion modelling as a tool in the exploration of other regression datasets.
Acknowledgement.
he assistance of Dr. Brian Miller of the Scottish Environment Protec-
tion Agency in gaining access to, and advising on, the data from the River Clyde is gratefully
acknowledged.
References
Adler, D. (
) he
R
package
rgl
:
D visualization device system (OpenGL) Ver-
sion
.
, available from cran.r-project.org.
Bock, M., Bowman, A.W. and Ismail, B. (
) Estimation and inference for error
variance in bivariate nonparametric regression. Technical report, Department of
Statistics, he University of Glasgow.
Bowman,A.W.andAzzalini,A.(
)AppliedSmoothingTechniquesforDataAnal-
ysis. Oxford University Press, Oxford.
Bowman, A.W. and Azzalini, A. (
) he
R
package
sm
: Smoothing methods for
nonparametric regression and density estimation. Version
.
-
, available from
cran.r-project.org.
