Estimator

Still don’t quite understand the differences. Confidence Interval

Estimates vs Estimators

Estimates: $\hat{\theta },\overline{y},\hat{\mu }$, etc → Calculated from samples Estimators: $\tilde{\theta }$ - a RV - $\overline{y_i}$ came from $\overline{Y}$ - estimator (like $\tilde{\theta }$)

Biased vs. Unbiased Estimators

Originally heard this from David Silver’s RL course the notes David Silver’s RL course the notes Monte-Carlo Learning. Also wrote about these ideas in David Silver’s RL course the notes Monte-Carlo Learning. Also wrote about these ideas in Monte-Carlo Learning. Also wrote about these ideas in Bootstrapping and Sampling.

Learning again through STAT206.

I think when it is an unbiased estimator, then you have that $E({\hat{\sigma }}^2)={\sigma }^2$

This is the kind of proffs that they do in Research Papers, and actually we barely covered it in class, file:///Users/stevengong/My%20Drive/Waterloo/2A/STAT206/Final/STAT206/Exam%20Practice%20Full%20Solutions.pdf is a good example.

From Confidence Interval, we say that $S^2$ is an unbiased estimator of ${\sigma }^2$, but ${\hat{\sigma }}^2$ is biased.