May 2015
Intermediate to advanced
384 pages
9h 20m
English
book
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
by Tailen Hsing, Randall Eubank
Content preview from Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
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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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