Hall, Peter; Gijbels, I; Kneip, Alois
Two-step methods are suggested for obtaining optimal performance in the problem of estimating jump points in smooth curves. The first step is based on a kernel-type diagnostic, and the second on local least-squares. In the case of a sample of size n the exact convergence rate is n-1, rather than n-1+δ (for some δ > 0) in the context of recent one-step methods based purely on kernels, or n-1(log n)1+δ for recent techniques based on wavelets. Relatively mild assumptions are required of the error...[Show more]
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