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3.1.7 Delta Method for Log Odds Ratio*
Standard errors for the log odds ratio and the log relative risk result from a multiparameter version of the delta method. Suppose that have a multinomial distribution. The sample proportion has mean and variance
and (3.7)
In Section 14.1.4 we show that for , and have covariance
(3.8)
The sample proportions have a large-sample multivariate normal distribution. For functions of them ,the delta method implies the following result, proved in Section 14.1.4:
Let denote a differentiable function of , with sample value for a multinomial sample. Let
Then as , the distribution of converges to standard normal, where
. (3.9)
The asymptotic variance depends on and the partial derivatives of the measure with respect to .In practice, replacing and in (3.9) by their sample v
Standard errors for the log odds ratio and the log relative risk result from a multiparameter version of the delta method. Suppose that have a multinomial distribution. The sample proportion has mean and variance
and (3.7)
In Section 14.1.4 we show that for , and have covariance
(3.8)
The sample proportions have a large-sample multivariate normal distribution. For functions of them ,the delta method implies the following result, proved in Section 14.1.4:
Let denote a differentiable function of , with sample value for a multinomial sample. Let
Then as , the distribution of converges to standard normal, where
. (3.9)
The asymptotic variance depends on and the partial derivatives of the measure with respect to .In practice, replacing and in (3.9) by their sample v
3.1.7 三角洲方法为日志可能性比率* 标准误差为日志可能性比率和日志相对风险起因于三角洲方法的multiparameter 版本。假设有多项式发行。样品比例有手段和变化 并且(3.7) 在部分14.1.4 我们显示那为, 和有协变性 (3.8) 样品比例有大样品多维分布的正常分配。为作用的他们, 三角洲方法暗示以下结果, 被证明在部分14.1.4: 让表示一个能区分的作用, 以样品价值为一个多项式样品。让 然后和, 发行聚合对标准法线, ．(3.9) 渐进变化依靠并且措施的部份衍生物谈到In 实践, 替换和(3.9) 由他们的样品价值出产量Then 的机器语言估计是一个估计的标准误差为A大样品Wald 信心间隔时间为是 ． 以代替为(3.9), 限制的发行是标准法线, bur 汇合是更慢的。相等在大样品发行被辩解如下: 样品比例聚合在可能性对,by 大数字微弱的法律。从是样品比例的一个连续函数, 它聚合在比例对, 和聚合在可能性到1 。现在 第一期限在右边聚合在发行对标准法线,(3.9), 并且第二个期限聚合在可能性对1.Thus, 他们的产品并且有限制的标准正常分配 我们向日志可能性比率现在运用三角洲方法, 采取since ．日志渐进标准误差为一个多项式样品是。 因为, 估计的标准误差是(3.1) 。 三角洲方法并且申请直接地与获得并且Wald 信心间隔时间This 不被推荐; 比日志对正常性, 这间隔时间能包含消极价值, 和它实行家不是授予结果等效与那些被获得以Wald 间隔时间使用和它的标准误差慢慢地聚合。