连续随机变量的随机独立与回归独立性的关系

The Relationship Between the Random Independence and the Return Independence of the Continuous Random Variant

回归独立性是指给定随机变量X是随机变量Y的条件期望E(Y|X)不依赖于X,前人讨论了离散型随机变量回归独立性的关系,得到了二者等价的充分必要条件。对连续型随机变量的情况加以讨论,获得了二者等价的几个充分必要条件,并说明在统计分析中的应用。

The return Independence refers to that the given random variant X is the Conditioned expectation. E （Y｜X） doesn＇t depend on X. Though the return independence of the dispersed random variant has been studied by many experts and the prerequisite for their equality has been proved , this essay will try to give more prerequisites and explain the application in statistics.