Let's say I have parameter $\{\theta_1, ..., \theta_T\} \in \Omega$. I estimate $\theta_{t+1}$ to be the average of its past history. Should the notation be: $\hat{\theta}_{t+1} = \frac{1}{t}\sum_{i=1}^{t} \theta_i$ or $E(\theta_{t+1}) = \frac{1}{t}\sum_{i=1}^{t} \theta_i$?
2026-03-30 17:39:38.1774892378
Difference between hat and expected value
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