Adaptive simultaneous confidence intervals in non-parametric estimation
We present non-linear wavelet methods to compute simultaneous confidence intervals for f(x) when f is a functional parameter issued from a non-parametric model. The levels of the intervals are at least [gamma], and we prove that they achieve the minimum diameter up to a logarithmic term. The procedure is data-driven and the adaptation is made via the Lepskii's algorithm.
Volume (Year): 69 (2004)
Issue (Month): 1 (August)
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- Hall, Peter & Titterington, D. M., 1988. "On confidence bands in nonparametric density estimation and regression," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 228-254, October.
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