Academic Phrase 2022.12.14

Any domain of interest for which there exists an invertible affine transformation that maps to [0,1]^p can be used, so that the transformation is performed, and then transformed back after the estimation, while retaining the non-crossing property.

直訳：[0,1]^pに写る可逆アフィン変換が存在する任意の関心領域が使用でき，非交差性を保持しながら，変換され，推定した後に逆変換が行われる．

Any domain of interest for which there exists an invertible affine transformation that maps to [0,1]^p can be used, so that the transformation is performed, and then transformed back after the estimation, while retaining the non-crossing property.

意訳：[0,1]^pに写る可逆アフィン変換が存在する任意の関心領域が使用でき，その領域では共変量を変換し，パラメータ推定後に逆変換で元の領域に写すことで，非交差性を保ったまま推定できる．

Reference

Bondell, H. D., Reich, B. J. and Wang, H. (2010). Noncrossing quantile regression curve estimation. Biometrika 97 825–38.