论文标题
Bi- $ s^*$ - 凹形发行
Bi-$s^*$-Concave Distributions
论文作者
论文摘要
我们在R，Bi-$ s^*$ - 凹面类上介绍了新的形状受限的分布功能。与杜姆登（Dümbgen），Kolesnyk和Wilke（2017）的结果平行，他们所谓的Bi-log-concave分发函数类别，我们表明，每个$ s $ concave concave ligenty $ f $都有bi- $ s^*$ - 凹形分配功能$ f $ for $ s^*\ s^*\ leq leq s+s+s+1）$。还考虑了建立在现有非参数乐队的基础上的信心带，但还考虑了双$ s^*$ - 凹的形状约束。新的频段扩展了Dümbgen等人开发的乐队。 （2017年）对双gog-concavity的限制。我们还建立了bi- $ s^*$ - csörgő-révész常数$ f $之间的连接，这在分数过程中起着重要作用。
We introduce new shape-constrained classes of distribution functions on R, the bi-$s^*$-concave classes. In parallel to results of Dümbgen, Kolesnyk, and Wilke (2017) for what they called the class of bi-log-concave distribution functions, we show that every $s$-concave density $f$ has a bi-$s^*$-concave distribution function $F$ for $s^*\leq s/(s+1)$. Confidence bands building on existing nonparametric bands, but accounting for the shape constraint of bi-$s^*$-concavity, are also considered. The new bands extend those developed by Dümbgen et al. (2017) for the constraint of bi-log-concavity. We also make connections between bi-$s^*$-concavity and finiteness of the Csörgő - Révész constant of $F$ which plays an important role in the theory of quantile processes.
