论文标题
惩罚双曲线分流量的繁殖能力
Reproduction Capabilities of Penalized Hyperbolic-polynomial Splines
论文作者
论文摘要
本文调查了双曲线分析性惩罚的两种重要分析特性，简称HP-Splines。通过将特殊类型的差异惩罚与双曲线级别B-Splines（HB-Splines）相结合的HP-Splines最近被作者作为P-Splines的概括引入。 Hb-Splines是由钟形的基础函数，由由真实指数制成的片段组成$ e^{αx}，\，e^{ - αx} $，线性函数乘以这些指数，$ xe^{+xe^{+αx} $和$ xe^^{ - αx} $。在这里，我们表明，这些类型的惩罚花键在空间中重现函数$ \ {e^{ - αx}，\ x e^{ - αx} \} $，即它们完全符合指数数据。此外，我们证明他们保留了第一个和第二个“指数”时刻。
This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines), were recently introduced by the authors as a generalization of P-splines. HB-splines are bell-shaped basis functions consisting of segments made of real exponentials $e^{αx},\, e^{-αx}$ and linear functions multiplied by these exponentials, $xe^{+αx}$ and $xe^{-αx}$. Here, we show that these type of penalized splines reproduce function in the space $\{e^{-αx},\ x e^{-αx}\}$, that is they fit exponential data exactly. Moreover, we show that they conserve the first and second 'exponential' moments.
