论文标题
pólya随机变量的凸点和伯恩斯坦 - 斯坦克操作员的误差估计值的单调性
Convex ordering of Pólya random variables and monotonicity of the error estimate of Bernstein-Stancu operators
论文作者
论文摘要
在本文中，我们表明，在Pólya的urn模型中，对于任意固定的urn的初始分布，相应的随机变量满足相对于替换参数的凸排序。作为一个应用程序，我们表明在凸函数类别中，伯恩斯坦 - 史密斯运算符的误差的绝对值是相应参数的非偏差（严格在附加假设下）的函数。 证明依赖于两个独立关注的结果：三组的交织引理以及Pólya随机变量（部分）相对于替换参数的（部分）第一刻的单调性。
In the present paper we show that in Pólya's urn model, for an arbitrarily fixed initial distribution of the urn, the corresponding random variables satisfy a convex ordering with respect to the replacement parameter. As an application, we show that in the class of convex functions, the absolute value of the error of Bernstein-Stancu operators is a non-decreasing (strictly increasing under an additional hypothesis) function of the corresponding parameter. The proof relies on two results of independent interest: an interlacing lemma of three sets and the monotonicity of the (partial) first moment of Pólya random variables with respect to the replacement parameter.
