Graphics Reference
In-Depth Information
Figure
.
.
Creating functional objects: price curves using penalized smoothing splines with p
=
and
λ
=
thefactthatobservedbidsdo not increasemonotonically duetoeBay'sproxybidding
system (Jank and Shmueli,
). hus, creating representative functional objects is
not a straightforward task.
Consider Fig.
.
. We can see that the functional objects are very “wiggly" and
certainly do not do a good job of representing the monotonic price increase in the
auction. Moreover, we also notice that some of the objects (e.g.,#
and #
) only par-
tially cover the seven-day period and thus do not represent the price evolution over
the entire auction. he reason for this is the sotware: the penalized spline module
pspline in R, by default, returns a function that is defined only on the range of the
input data. Hence, since the bids for #
and #
cover only a small part of the du-
ration of the auction, so does the resulting functional object. Lastly, we notice that
there are no functional objects for #
and #
. he reason for this is that the pspline
module requires at least
p
data points to estimate a smoothing spline of order p.
his means that for a second-order smoothing spline we need at least
+
points. However,both #
and#
only havethree bidsandthus nofunctional object is
created. his loss of information is quite disturbing from a conceptual point of view,
sincedataareinfactavailableforthesetwoauctionsandthemissing(functional)data
are a consequence of the functional object generation process. In summary, if the re-
searcher were to use the smoothing approach from Fig.
.
“blindly" (i.e., without
(
)(
)+
=
