Graphics Reference
In-Depth Information
focuses only on the variation that is not explained by the others. Some interesting
features are displayed in the curve estimates, with DO declining in a linear manner
as temperature increases while DO is elevated at low salinity but constant elsewhere.
Reassuringly, the trend across years remains very similar to the patterns displayed in
earlier analysis, when adjustment involved only the day of the year. his collection
of graphs therefore provides a very powerful summary of the data across all the co-
variates involved andbrings considerable insight intothe factorswhichinfluence the
observed values of DO.
Discussion
9.5
he material of this chapter has aimed to introduce the concepts and aims of non-
parametric regression as a means of adding significant value to graphical displays of
data. Technical details have been limited only to those required to give a general ex-
planation of the methods. However, a great deal of technical work has been carried
out on this topic,which is well represented in the statistical research literature. here
are several topics in this area and these provide good starting points for further in-
formation. Hastie and Tibshirani (
) give a good general overview of smoothing
techniques as well as a detailed treatment of additive models. Green and Silverman
(
) give a very readable and integrated view of the penalty function approach to
smoothing models. Fan and Gijbels (
)gives considerable theoretical insight into
the local linear approach to smoothing, while Simonoff (
) is particularly strong
in providing extensive references to the literature on nonparametric regression and
is therefore a very good starting point for further reading.
Bowman and Azzalini (
) give a treatment which aligns most closely with the
style of exposition in this chapter and focuses particular attention on smoothing
over one and two covariates and on graphical methods. Schimek (
) provides
an collection of contributions from a wide variety of authors on different aspects
of the topic. Härdle et al. (
) give a further general overview of nonparametric
modelling, while Ruppert et al. (
) give an authoritative treatment of semipara-
metric regression in particular. Wood (
) provides an excellent introduction to,
andoverview of,additive models,focussinginparticular onthe penalized regression
splinesframeworkandwithagreatdealofhelpfulpracticaldiscussion.Analternative
wavelet view of modelling is provided by Percival and Walden (
) in the context
oftimeseriesanalysis. Onspecifically graphical issues,Cleveland (
)makesexcel-
lent use of smoothing techniques in the general context of visualising data. Material
provided by Loader (
) on local regression techniques and Horowitz (
) on
semiparametric models in an earlier Handbook of Computational Statistics are also
highly relevant to the material of this chapter.
he role of smoothing techniques in visualisation has been indicated by specific
regression examples inthis chapter.However,the principlesbehindthis approachal-
low it to be applied to a very wide range of data structures and application areas. For
example, Cole and Green (
)discussthe estimation of quantile curves, while Kim
