Penalized logspline density estimation using total variation penalty

Kwan-Young Bak, Jae-Hwan Jhong, JungJun Lee, Jae-Kyung Shin and Ja-Yong Koo

Computational Statistics & Data Analysis, 2021, vol. 153, issue C

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 bona fide 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.

Keywords: B-spline; Coordinate descent algorithm; Kullback–Leibler divergence; Optimal convergence rate; Oracle inequality (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:153:y:2021:i:c:s0167947320301511

DOI: 10.1016/j.csda.2020.107060

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