I am interested in the estimator of the mean of the gamma distribution. I need to calculate the CRLB for this estimator. How can this be done, since the mean is $\kappa\theta$ (2 parameters). I consider the following possibilities:
- Use the multivariate version of the CRLB. I think this is the right solution, but I am wondering if I can use the one-dimensional CRLB.
- Consider one parameter constant. However, which one?
- Substitute $\kappa\theta$ by for example $\mu$, since I want to estimate this parameter. However, then the likelihood will still be depending on 2 parameters, leading to idea 2. For example, I substitute $\theta$ for $\frac{\mu}{\kappa}$ and need to assume $\kappa$ constant.
Hope you can give clear insight!
Thank you