Two sample inference for the mean and covariance functions
Due to possibly different FPC’s structures, working with two functional samples may be difficult. An important contribution has been made by Benko et al. (2009) who developed bootstrap procedures for testing the equality of mean functions, the FPC’s, and the eigenspaces spanned by them. In this chapter, we present asymptotic procedures for testing the equality of the means and the covariance operators in two independent samples. Section 5.1 focuses on testing the equality of mean functions. It shows that instead of statistics which have chi–square limits, those that converge to weighted sums of squares of independent standard normals can also be used. In other chapters we focus on statistics converging to chi–square distributions, but analogous versions converging to weighted sums of normals can be readily constructed.
KeywordsCovariance Function Covariance Operator Nominal Size Brownian Bridge Schmidt Operator
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