Anisotropic local constant smoothing for change-point regression function estimation

12/01/2020 ∙ by John R. J. Thompson, et al. ∙ 0

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(n^-1/(q+2)). We demonstrate its effectiveness on simulated one- and two-dimensional change-point data and fire spread imagery from micro-fire experiments.

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