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Penalized log-density estimation using Legendre polynomials

Authors
Lee, JungJunJhong, Jae-HwanCho, Young-RaeKim, SungHwanKoo, Ja-Yong
Issue Date
1-11월-2020
Publisher
TAYLOR & FRANCIS INC
Keywords
Penalized log-density estimation; nonparametric density estimation; Legendre polynomial basis; coordinate descent algorithm; l(1) penalty; maximum tuning parameter
Citation
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, v.49, no.11, pp.2844 - 2860
Indexed
SCIE
SCOPUS
Journal Title
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
Volume
49
Number
11
Start Page
2844
End Page
2860
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/130378
DOI
10.1080/03610918.2018.1528360
ISSN
0361-0918
Abstract
In this article, we present a penalized log-density estimation method using Legendre polynomials with l(1) penalty to adjust estimate's smoothness. Re-expressing the logarithm of the density estimator via a linear combination of Legendre polynomials, we can estimate parameters by maximizing the penalized log-likelihood function. Besides, we proposed an implementation strategy that builds on the coordinate decent algorithm, together with the Bayesian information criterion (BIC). In particular, we derive a numerical solution to the maximum tuning parameter lambda(max) which leads to all zero coefficients and practically facilitates searching the optimal tuning parameter. Extensive simulation studies clearly show that our proposed estimator is computationally competitive with other existing nonparametric density estimators (e.g., kernel, kernel smooth and logspline estimators) benchmarked by the mean integrated squared errors (MISE) and the mean integrated absolute error (MIAE) under the experiment scenario of separated bimodal models in regard to the true density function. With an application to Old Faithful geyser data, our proposed method is found to effectively perform density estimation.
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