8.3 Penalized least-squares estimation
Section 8.2 considered nonparametric estimation of the mean function and covariance kernel using local linear regression type estimators. In this section, we explore a slightly different development with smoothing spline variants as the estimators of choice.
The model to be considered is much the same as (8.2) with 
iid as some second-order stochastic process 
on 
. As before, let 
and 
be the mean and covariance functions of 
. For simplicity, we will focus attention on the case where the 
are a random sample from the uniform distribution. Apart from that, the major difference is that we now assume that 
is a random element of the Sobolev space described ...
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