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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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Chapter 8Mean and covariance estimation

In this chapter, we study mean and covariance estimation for both the random element and stochastic process settings described in Chapter 7. For the first perspective, let c08-math-001 be a separable Hilbert space and suppose that we have a random element c08-math-002 of c08-math-003 with c08-math-004. The mean element and covariance operator of c08-math-005 from Section 7.2 are therefore well defined as

equation

and

equation

In Section 8.1, we address the base problem of estimating c08-math-006 and c08-math-007 using a random sample c08-math-008 from . The estimators ...

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