摘要：P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_{2}$ norm. P-splines can be used for semiparametric regression and can include random effects to account for within-subject correlations. In addition to $\ell_{2}$ penalties, $\ell_{1}$-type penalties have been used in nonparametric and semiparametric regression to achieve greater flexibility, such as in locally adaptive regression splines, $\ell_{1}$ trend filtering, and the fused lasso additive model. However, there has been less focus on using $\ell_{1}$ penalties in P-splines, particularly for estimating conditional means.
