polygram swMATH ID: 44817 Software Authors: Jhong, Jae-Hwan; Bak, Kwan-Young; Koo, Ja-Yong Description: Penalized polygram regression. We consider a study on regression function estimation over a bounded domain of arbitrary shapes based on triangulation and penalization techniques. A total variation type penalty is imposed to encourage fusion of adjacent triangles, which leads to a partition of the domain consisting of disjointed polygons. The proposed method provides a piecewise linear, and continuous estimator over a data adaptive polygonal partition of the domain. We adopt a coordinate decent algorithm to handle the non-separable structure of the penalty and investigate its convergence property. Regarding the asymptotic results, we establish an oracle type inequality and convergence rate of the proposed estimator. A numerical study is carried out to illustrate the performance of this method. An R software package polygram is available. Homepage: https://link.springer.com/article/10.1007/s42952-022-00181-5 Dependencies: R Keywords: barycentric coordinates; coordinate descent algorithm; minimaxity; polygonal partitions; triangulation Related Software: ConstrainedLasso; fields; Triangle; R; ISLR Cited in: 1 Document Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Penalized polygram regression. Zbl 07643159Jhong, Jae-Hwan; Bak, Kwan-Young; Koo, Ja-Yong 2022 Cited by 3 Authors 1 Bak, Kwan-Young 1 Jhong, Jae-Hwan 1 Koo, Ja-Yong Cited in 1 Serial 1 Journal of the Korean Statistical Society Cited in 1 Field 1 Statistics (62-XX) Citations by Year