z*******9
发帖数: 167 | 1 【 以下文字转载自 Quant 讨论区 】
发信人: sly (伸懒腰), 信区: Quant
标 题: Re: 一道很有意思的老题: some thought
发信站: BBS 未名空间站 (Tue Aug 10 10:58:19 2010, 美东)
Thank you for your reply. I thought about it last night and worked out a
similar solution as well:
error rate=E[G(X1)*(1-F(X1))+(1-G(X1))*F(X1)], one thing to note here is
that the expectation is taken on F. then:
error rate = Integral {F(X)dF(X)}+Integral{G(X)dF(X)-2*G(X)*F(X)dF(X)}
=0.5+Integral{(G(X)*d(F(X)-F(X)^2)}
=0.5-Integral{(F(X)-F(X)^2)dG | z*******9
发帖数: 167 | 2 一个似乎不可能的结论，居然被严格证明了。
【在 z*******9 的大作中提到】
: 【 以下文字转载自 Quant 讨论区 】
: 发信人: sly (伸懒腰), 信区: Quant
: 标 题: Re: 一道很有意思的老题: some thought
: 发信站: BBS 未名空间站 (Tue Aug 10 10:58:19 2010, 美东)
: Thank you for your reply. I thought about it last night and worked out a
: similar solution as well:
: error rate=E[G(X1)*(1-F(X1))+(1-G(X1))*F(X1)], one thing to note here is
: that the expectation is taken on F. then:
: error rate = Integral {F(X)dF(X)}+Integral{G(X)dF(X)-2*G(X)*F(X)dF(X)}
: =0.5+Integral{(G(X)*d(F(X)-F(X)^2)}
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