Estimator

Topics: Statistics - Sample Statistic

---

(definition)

An estimator is a sample statistic that aims to estimate a given parameter of the random sample at hand.

More formally, given a random variable $X$ and its corresponding random sample $X_1,X_2,\dots ,X_n$ characterised by a parameter $\theta$, an estimator $\hat{\theta }$ is a function $\hat{\theta }(X)=f(X_1,X_2,\dots ,X_n)$ that returns an approximation of $\theta$.

Quality §

Of course, not all estimators for a same parameter are the same.

For instance, there can be unbiased, asymptotically unbiased, efficient, consistent and uniformly minimum-variance unbiased (UMVUE) estimators, to name just a few.

We generally prefer unbiased, efficient and minimum-variance estimators, since they tend to give a better approximation to the actual value of the parameter.