Confidence Bands for the Gradient Lines of a Density Function

Ery Arias-Castro; Wanli Qiao

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arXiv · 2606.14087

Confidence Bands for the Gradient Lines of a Density Function

Ery Arias-Castro·Wanli Qiao

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Abstract

We consider the problem of estimating the gradient ascent line of a density originating at a given point. Going beyond mere consistency, we establish a weak convergence result for a plugin estimator based on a kernel density estimator of the density. We then leverage that result to construct a confidence region for the gradient ascent line, including by bootstrap.

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Ery Arias-Castro, Wanli Qiao. 2026-06-12. Confidence Bands for the Gradient Lines of a Density Function. https://arxiv.org/abs/2606.14087

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