Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method
J. Lars Kirkby,
Álvaro Leitao and
Duy Nguyen
Computational Statistics & Data Analysis, 2021, vol. 159, issue C
Abstract:
A general and efficient nonparametric density estimation procedure for local bases, including B-splines, is proposed, which employs a novel statistical Galerkin method combined with basis duality theory. To select the bandwidth, an efficient cross-validation procedure is introduced, based on closed-form expressions in terms of the primal and dual B-spline basis. By utilizing a closed-form expression for the dual basis, the least-squares cross validation formula is calculated in closed-form, enabling an efficient estimation of the optimal bandwidth. The full computational procedure achieves optimal complexity, and is very accurate in comparison with existing estimation procedures, including state-of-the-art kernel density estimators. The presented theoretical results are supported by extensive numerical experiments, which demonstrate the efficiency and accuracy of the new methodology. This new approach provides a complete and optimally efficient framework for density estimation with a B-spline basis, based on simple and elegant closed-form estimators with theoretical convergence results that are substantiated in numerical experiments.
Keywords: Nonparametric density estimation; Spline; Bandwidth; Kernel; Basis; Cross-validation (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:159:y:2021:i:c:s0167947321000360
DOI: 10.1016/j.csda.2021.107202
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