2

I am looking for an estimation/iteration process to estimate the value of a specific unobserved parameter of a convex function that fits the observed data of the other variables closely. Specifically, in the following equation b, v, r and n are observed through an experimental procedure and I would like to estimate the value of α that fits the data most closely. Note that this equation was derived from an optimization problem.

\begin{align} b &= v-\frac{av^\frac{n+a-1}{a}-ar^\frac{n+a-1}{a}}{(n+a-1)v^\frac{n-1}{a}} \end{align}

Koula
  • 21
  • 2
  • Is $a$ the same thing as $\alpha$? – Eli Feb 09 '22 at 14:45
  • Also, you tagged this post with `identifiability`. Do you believe some of the parameters are not identifiable? I don't see any identifiability issues but I could be wrong. – Eli Feb 09 '22 at 14:47
  • Yes, there are the same thing! Sorry for the confusion! I do believe that there is point identification, maybe wrongly I tagged the post with identifiability. Actually, I am searching for a method to estimate it. – Koula Feb 09 '22 at 15:30
  • Can you subtract $b$ from both sides of the equation then find where the equation is 0? – Eli Feb 09 '22 at 15:34
  • Is there an error term in your equation? E.g. $b = f(a; b, v, r, n) + \epsilon$ – Eli Feb 09 '22 at 15:36
  • I cannot solve for the parameter α. I am searching for the value of the unobserved parameter α that fits closely the data on the observed parameters of b, v, r and n based on this equation. – Koula Feb 09 '22 at 15:45
  • No, there is not. This equation was derived from an optimization problem (first order condition) and solved for b. – Koula Feb 09 '22 at 15:48
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/133990/discussion-between-koula-and-eli). – Koula Feb 09 '22 at 15:54

0 Answers0