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Wang, Dongying

University of British Columbia

Data sharpening is a semiparametric method that is more flexible than parametric regression and is less variable than nonparametric regression. We study two kinds of data sharpening for local polynomial regression in this thesis. One version is penalized data sharpening, which constrains the regression function estimate globally. The other is constrained data sharpening, which operates more locally. Each approach requires a good bandwidth. Implementation details for direct-plug-in bandwidth selection for local linear regression are reviewed and extended to higher order local polynomial regression. The next critical step in solving the penalized data sharpening problem is to select a good tuning parameter. In this thesis, we propose and study several tuning parameter selectors. For constrained data sharpening, we study the optimization problem and solve it numerically using the Douglas-Rachford algorithm. By combining with the backfitting algorithm, we can apply the constrained data sharpening method to higher dimensional data, where our focus is on additive models. We apply penalized data sharpening and constrained data sharpening methods to some real data such as wildfire rate of spread data, temperature data, and images extracted from videos of small smoldering fires.

Text

2022-08-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/82617

Mathematics

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/