smoothness. In the process of evaluating the function given data, it is very
likely that the two cost measures are somewhat at odds with each other. If
we decide to fit the functional form very closely to the data, then we may
have to give some slack on the degree of smoothness of the data. However,
if we adhere strongly to the notion that the function is smooth, we may have
to sacrifice on the agreement of the function to the data. The choice of the
function therefore involves a delicate balancing act between the two cost
measures. Note that the previously mentioned idea can also be couched in
terms of the classic and ubiquitous notion in statistics of the compromise be-
tween goodness of fit and bias. If the reader is thinking that the idea has a
familiar ring to it, it is probably because we visited this notion before in
Chapter 2 (and you can be sure that you will read of this again in the book).
Depending on the nature of the second cost measure that relates to the
property of the function being estimated, regularization is referred to by
Trading Design 131
FIGURE 8.4 Raw Counts Adjusted for Monotonicity.Amount of Sigma Away from Mean0.000.150.300.450.600.750.901.051.201.351.501.651.801.922.100.0
0.2
0.1
0.3
0.4
0.5
Raw Counts
Monotonic Adjustment