Testing for the mean of random curves: A penalization approach

Let X 1,...,X n be an i.i.d. sample of random curves, viewed as Hilbert space valued random elements, with mean curve m. An asymptotic test of m = m 0 vs m ≠ m 0 is proposed, when m 0 is a fixed known function. The test statistics converges under very mild assumptions and relies on the pseudo-inversion of the covariance operator (leading to a non standard inverse problem). The power against local alternatives is investigated. © Springer 2006.