Testing for the mean of random curves : a penalization approach

Andre Mas (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

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 6 = m 0 is proposed, when m 0 is a …xed 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.

Mots clés: Random curves; functional data; weak convergence; hypothesis testing; local alternatives

Domaines: Statistiques [math.ST]

Andre Mas. Testing for the mean of random curves : a penalization approach. Statistical Inference for Stochastic Processes, 2007, 10 (2), pp.147 - 163. ⟨10.1007/s11203-005-0754-3⟩. ⟨hal-01817402⟩