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Adaptive simultaneous confidence intervals in non-parametric estimation

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  • Tribouley, Karine

Abstract

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.

Suggested Citation

  • Tribouley, Karine, 2004. "Adaptive simultaneous confidence intervals in non-parametric estimation," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 37-51, August.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:1:p:37-51
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    References listed on IDEAS

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    1. 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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