Graphics Reference
In-Depth Information
Another reason to explore the data is to investigate the distributions of individual
variables. Since most parametric models require the response to follow a certain dis-
tribution (typically the normal distribution), this step is important for selecting the
right model and for ensuring the appropriateness of the selected model. One stan-
dard tool for investigating the distribution of a numerical variable is the histogram.
However,generalizing the ideaofahistogram to the functional context isachalleng-
ing task, since the input variable is a continuous function. One solution is to graph
the distribution of the functional object at only a few select snapshots in time. his
can be done by discretizing the object and graphing pointwise histograms (or simi-
lar plots such as probability plots) at each time point. Figure
.
shows snapshots of
the distributions of the
eBay price curves at days
,
and
. hese snapshots allow
conclusions to bedrawn about the distribution of the entire functional object. Notice
that Fig.
.
also shows kernel density estimates of the distributions and thus allows
conclusions to be drawn about the evolution of the functional density over days
-
.
One can generalize this idea to obtain the density continuously over the entire func-
tional object (rather than only at discretetime points). Specifically, Fig.
.
showsthe
density estimates evaluated over a fine grid and subsequently interpolated. We can
see that the distribution is very flat at the beginning of the auction and it starts to
peak towards the end.
Figure
.
.
Contour plot of the density of the functional objects over the seven-day auction. he
contour plot is obtained by calculating kernel density estimates (as done in Fig.
.
) over a fine grid and
subsequent interpolation over the seven-day period
