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arXiv Statistics ML By Bal\'azs Csan\'ad Cs\'aji, B\'alint Horv\'ath

MiNCE: Nonparametric, Strongly Consistent Confidence Envelopes for Band-Limited Functions and their Smoothed Spectra

Read the original on arXiv Statistics ML →

The paper introduces MiNCE, a nonparametric framework for constructing minimum‑norm confidence envelopes that provide nonasymptotic, simultaneous confidence regions for band‑limited functions using Reproducing Kernel Hilbert Spaces. It proves strong uniform consistency of these envelopes for both noise‑free and noisy data under mild noise assumptions, and extends the results to the frequency domain to yield consistent confidence bands for smoothed spectra. Numerical experiments in nonparametric regression and spectral estimation confirm the theoretical findings, showing the envelopes contract toward the target function as sample size grows.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Statistics ML.

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