For starters, we have:
Stated as an alpha-risk, that's
Since the denominator is always positive, this implies
so, collecting all the stuff that changes each sample on the left, we stop when
Saturday, November 11, 2017
Stopping rule revisited
So, my stopping rule got a little contorted through all the various machinations of my variance. Fortunately, I had it right in the code all along, I just transcribed it badly when going from the confidence interval to the stopping rule (basically, I stop when the confidence interval is sufficiently narrow).
For starters, we have:
}}&space;=&space;Z\sim&space;N(0,1) "\frac{Y-Y^r}{\hat\sigma\sqrt{\frac{n}{r}(n-r)}} = Z\sim N(0,1)")
Stated as an alpha-risk, that's
&space;=&space;\textup{P}\left(\frac{|Y-Y^r|}{\hat\sigma\sqrt{\frac{n}{r}(n-r)}}&space;\le\frac{B}{\hat\sigma\sqrt{\frac{n}{r}(n-r)}}\right) "\alpha \le \textup{P}(|Y-Y^r| < B) = \textup{P}\left(\frac{|Y-Y^r|}{\hat\sigma\sqrt{\frac{n}{r}(n-r)}} \le\frac{B}{\hat\sigma\sqrt{\frac{n}{r}(n-r)}}\right)")
Since the denominator is always positive, this implies
}} "Z_{a/2} \le \frac{B}{\hat\sigma\sqrt{\frac{n}{r}(n-r)}}")
so, collecting all the stuff that changes each sample on the left, we stop when
}&space;\le&space;\frac{B}{Z_{a/2}} "\hat\sigma\sqrt{\frac{n}{r}(n-r)} \le \frac{B}{Z_{a/2}}")
For starters, we have:
Stated as an alpha-risk, that's
Since the denominator is always positive, this implies
so, collecting all the stuff that changes each sample on the left, we stop when
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment