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Penalized logspline density estimation using total variation penalty

Authors
Bak, Kwan-YoungJhong, Jae-HwanLee, JungJunShin, Jae-KyungKoo, Ja-Yong
Issue Date
1월-2021
Publisher
ELSEVIER
Keywords
B-spline; Coordinate descent algorithm; Kullback-Leibler divergence; Optimal convergence rate; Oracle inequality
Citation
COMPUTATIONAL STATISTICS & DATA ANALYSIS, v.153
Indexed
SCIE
SCOPUS
Journal Title
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume
153
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/50205
DOI
10.1016/j.csda.2020.107060
ISSN
0167-9473
Abstract
We study a penalized logspline density estimation method using a total variation penalty. The B-spline basis is adopted to approximate the logarithm of density functions. Total variation of derivatives of splines is penalized to impart a data-driven knot selection. The proposed estimator is a bonafide density function in the sense that it is positive and integrates to one. We devise an efficient coordinate descent algorithm for implementation and study its convergence property. An oracle inequality of the proposed estimator is established when the quality of fit is measured by the Kullback-Leibler divergence. Based on the oracle inequality, it is proved that the estimator achieves an optimal rate of convergence in the minimax sense. We also propose a logspline method for the bivariate case by adopting the tensor-product B-spline basis and a two-dimensional total variation type penalty. Numerical studies show that the proposed method captures local features without compromising the global smoothness. (C) 2020 Elsevier B.V. All rights reserved.
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