论文标题
Edgeworth扩展Bernoulli加权平均
Edgeworth expansion for Bernoulli weighted mean
论文作者
论文摘要
在这项工作中，我们得出了bernoulli加权的Edgeworth扩展，$ \hatμ= \ frac {\ sum_ {\ sum_ {i = 1}^n y_i t_i} {\ sum_ {\ sum_ {i = 1}^n t_i} $在其中$ y_1，y_1，dots，y_n $ i.i.i.i.i.i.d.非半晶格随机变量和$ t_1，\ dots，t_n $是带有参数$ p $的bernoulli分布式随机变量。 We also define the notion of a semi-lattice distribution, which gives a more geometrical equivalence to the classical Cramér's condition in dimensions bigger than 1. Our result provides a first step into the generalization of classical Edgeworth expansion theorems for random vectors that contain both semi-lattice and non semi-lattice variables, in order to prove consistency of bootstrap methods in more realistic setups, for instance in the use在线AB测试的情况。
In this work, we derive an Edgeworth expansion for the Bernoulli weighted mean $\hatμ = \frac{\sum_{i=1}^n Y_i T_i}{\sum_{i=1}^n T_i}$ in the case where $Y_1, \dots, Y_n$ are i.i.d. non semi-lattice random variables and $T_1, \dots, T_n$ are Bernoulli distributed random variables with parameter $p$. We also define the notion of a semi-lattice distribution, which gives a more geometrical equivalence to the classical Cramér's condition in dimensions bigger than 1. Our result provides a first step into the generalization of classical Edgeworth expansion theorems for random vectors that contain both semi-lattice and non semi-lattice variables, in order to prove consistency of bootstrap methods in more realistic setups, for instance in the use case of online AB testing.
