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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Randall Eubank, Tailen Hsing

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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 c08-math-346 iid as some second-order stochastic process c08-math-347 on c08-math-348. As before, let c08-math-349 and c08-math-350 be the mean and covariance functions of c08-math-351. For simplicity, we will focus attention on the case where the c08-math-352 are a random sample from the uniform distribution. Apart from that, the major difference is that we now assume that c08-math-353 is a random element of the Sobolev space described ...

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