Timeline for Estimate true mean of the maximum of N sample means
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 8, 2019 at 12:09 | comment | added | aagold | Thanks so much for your response and edits, stats_model. This was my first question on stack exchange... This seems like a great community! | |
| S Apr 8, 2019 at 11:21 | history | suggested | stats_model | CC BY-SA 4.0 |
Formatting with TeX to make question more readable; changed wording to be more mathematically correct (in particular, a distribution and a random variable are different)
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| Apr 8, 2019 at 4:19 | comment | added | stats_model | By continuous mapping theorem, however, it is easy enough to show that if your asymptotics fix $N$ and let $M \to \infty$, your proposed estimator will be consistent (you don't even need normality for this). | |
| Apr 8, 2019 at 4:12 | comment | added | stats_model | Your proposed estimator certainly won't be unbiased in general, as demonstrated with the following counterexample. Consider $N = 2$ and suppose WLOG that $\mu_1 > \mu_2$. Then $E[m_{i_{max}}] = E[E[\max(m_1, m_2) | m_2]] >E[\max(E[m_1 | m_2], m_2)] = E[\max(\mu_1,m_2)] >\max(\mu_1, E[m_2]) = \mu_1$ where I used convexity of $\max$ and Jensen's inequality. | |
| Apr 8, 2019 at 3:56 | review | Suggested edits | |||
| S Apr 8, 2019 at 11:21 | |||||
| Apr 8, 2019 at 2:55 | review | Close votes | |||
| Apr 9, 2019 at 22:17 | |||||
| Apr 8, 2019 at 1:40 | review | First posts | |||
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| Apr 8, 2019 at 1:35 | history | asked | aagold | CC BY-SA 4.0 |