Timeline for Error exponent in hypothesis testing
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7, 2012 at 6:57 | comment | added | Ashok | @Michele: Yeh, sorry. I just overlooked the things. Very good discussion. I got to know several things from this. Thank you. | |
| Jan 6, 2012 at 18:55 | comment | added | Michele | @Ashok: in your example, write en as $$\pi_2e^{−bn}(\frac{\pi_1}{\pi_2}e^{−(a−b)n}+1)$$ then take the $-\frac 1 n \log$: the limit is $b$, not $a+b$. This is not the bug in the reasoning: see my post and the discussion at stats.stackexchange link. | |
| Jan 6, 2012 at 11:35 | comment | added | Ashok | Why should $\lim -\frac 1 n \log e_n = \min{\lim -\frac 1 n \log \alpha_n, \lim -\frac 1 n \log \beta_n}$? Suppose $\alpha_n \approx e^{-an}$ and $\beta_n \approx e^{-bn}$ for some $a>b>0$ and $\pi_1=1/2=\pi_2$ then the l.h.s. is $a+b$ whereas the r.h.s. is $b$. | |
| Jan 5, 2012 at 19:44 | history | asked | Michele | CC BY-SA 3.0 |