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

2026-09-08

AI Summary

本文提出MiNCE框架，利用RKHS理论构建带限函数及其平滑谱的一致性置信包络，并证明了其在无噪声和有噪声观测模型下的强一致性。

Abstract

Minimum-norm confidence envelope strategies offer a nonparametric approach to constructing nonasymptotic, simultaneous confidence regions for band-limited functions, exploiting the theory of Reproducing Kernel Hilbert Spaces (RKHS). While the finite-sample coverage guarantees of these envelopes have been established, their consistency has not been analyzed so far. In this paper, we study this construction, here termed the Minimum-Norm Confidence Envelope (MiNCE) framework, and establish the strong uniform consistency of the resulting bands, both for noise-free and noisy observation models, under mild assumptions on the measurement noises. We further extend this formulation to the frequency domain, deriving nonasymptotic, simultaneous, strongly uniformly consistent confidence bands for the smoothed spectra. Numerical experiments in nonparametric regression and spectral estimation empirically confirm our theoretical results, illustrating the contraction of the confidence envelopes toward the target function as the sample size increases.

Problem

• Minimum-Norm Confidence Envelope
• band-limited functions
• smoothed spectra
• strong uniform consistency

Innovation

• Minimum-Norm Confidence Envelope
• Reproducing Kernel Hilbert Spaces
• strong uniform consistency
• band-limited functions
• smoothed spectra