Estimation
Estimation uses sample data to infer unknown characteristics of a population or statistical model.
An estimator \(\hat\theta\) is a random quantity calculated from the data and used to estimate a parameter \(\theta\).
Bias
An estimator is unbiased when
\[E[\hat\theta]=\theta.\]Precision
Two unbiased estimators may have different variances. Smaller variance means estimates fluctuate less across repeated samples.
Point and interval estimation
A point estimate gives a single value. An interval estimate expresses uncertainty around the inferred quantity.
Key idea. Estimation concerns both the value inferred from data and the uncertainty or sampling behaviour of the method used to infer it.