Timeline for Binomial Expectation of Convex Function
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 29, 2015 at 22:13 | comment | added | Stefan Kohl♦ | This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. | |
| Oct 4, 2013 at 21:20 | comment | added | Michael Hardy | So $\alpha^*(y)$ is the value of $\alpha$ for which the bias of $f(x)$ as an estimator of $\alpha$ is $y$. | |
| Oct 4, 2013 at 21:19 | comment | added | Michael Hardy | +1. I changed \;|\; to \mid. I think that is standard. | |
| Oct 4, 2013 at 21:16 | comment | added | Michael Hardy | The notation $\mathbb E[f(x)\mid\alpha]$ is a way of writing the expected value in which its dependence on $\alpha$ is given a place in the notation, so that, for example, one can write expressions like $\mathbb E[f(x)\mid\alpha]/\mathbb E[f(x)\mid\alpha_0]$. Suppose that 20 pages after you first write about the random variable $x$ whose distribution depends on $\alpha$, it becomes appropriate to assign a probability distribution to $\alpha$. Then the notation refers to the conditional expected value while remaining consistent with the way it was used earlier. | |
| Oct 4, 2013 at 21:09 | history | edited | Michael Hardy | CC BY-SA 3.0 |
added 3 characters in body
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| S Sep 4, 2013 at 17:08 | comment | added | user39430 | Lots of other nice properties are derived in this paper, and the answers to that question offer some further reading. Edit: See also mathoverflow.net/questions/122897/… which has much more analysis of this type. | |
| S Sep 4, 2013 at 17:08 | comment | added | user39430 | What does the notation $\mathbb{E}[ \cdot \mid \alpha]$ mean? Please tell us more about what this problem is for, but the paper referenced at mathoverflow.net/questions/21858/… by Sah ("The Effects of Child Mortality Changes on Fertility Choice and Parental Welfare", equations 4 - 7) offers a property which sufficed for a similar problem I was tackling. Namely, \begin{align*} \frac{\partial}{\partial \alpha} \mathbb{E}[f(x)] = k \cdot \sum_{j=0}^{k-1} {k-1 \choose j} \alpha^j (1-\alpha)^{k-1-j} (f(x+1)-f(x)). \end{align*} (cont.) | |
| Feb 3, 2013 at 0:25 | history | asked | Josh | CC BY-SA 3.0 |