Iam stuck on something, probably simple, it is in a proof: Suppose there is a parameter $\psi$ of interest that can be expressed linearly in the canonical parameter $\theta$, so we may represent $\theta$ as $(\lambda,\psi)$.. suppose $\theta = (\frac{\mu}{\sigma^2},-\frac{1}{2\sigma^2} )$ can we express $\sigma^2$ linearly in $\theta$? can we express $\mu$ linearly in $\theta$ , how? can some one showme
This example(from my book) illustrates the sufficiency principle and I will write it down so that you get some context :
Let $\boldsymbol{X} = (X_1,X_2..,X_n)$ be a sample of independent bernoulli variables then the probability function is:
$p(\boldsymbol{x};\theta) = \prod\limits_{i=1}^{i=n}\t...
This example(from my book) illustrates the sufficiency principle and I will write it down so that you get some context :
Let $\boldsymbol{X} = (X_1,X_2..,X_n)$ be a sample of independent bernoulli variables then the probability function is:
$p(\boldsymbol{x};\theta) = \prod\limits_{i=1}^{i=n}\t...