Anisotropic local constant smoothing for change-point regression function estimation

TL;DR

This paper introduces an anisotropic local constant smoothing method for change-point regression, providing a statistically consistent estimator that effectively denoises fire spread imagery from micro-fire experiments.

Contribution

It develops a novel anisotropic smoothing technique for change-point data that leverages data-driven estimates to improve denoising accuracy and consistency.

Findings

Estimator is statistically consistent with convergence rate $O(n^{-1/(q+2)})$

Effective on simulated change-point data

Successfully denoises fire spread imagery from experiments

Abstract

Understanding forest fire spread in any region of Canada is critical to promoting forest health, and protecting human life and infrastructure. Quantifying fire spread from noisy images, where regions of a fire are separated by change-point boundaries, is critical to faithfully estimating fire spread rates. In this research, we develop a statistically consistent smooth estimator that allows us to denoise fire spread imagery from micro-fire experiments. We develop an anisotropic smoothing method for change-point data that uses estimates of the underlying data generating process to inform smoothing. We show that the anisotropic local constant regression estimator is consistent with convergence rate $O\left(n^{-1/{(q+2)}}\right)$. We demonstrate its effectiveness on simulated one- and two-dimensional change-point data and fire spread imagery from micro-fire experiments.