Statistic

Definition

Let $X_1,\dots ,X_n$ : Random sample

If $T=T(X_1,\dots ,X_n)$, function of random samples

Then we say $T$ is a statistic of $X_1,\dots ,X_n$

Remark

Once the sample is drawn, then we denote the realization of $T$ as $t$, where $t=T(x_1,\dots ,x_n)$, and $x_1,\dots ,x_n$ is the realization of the random sample.

Subdefinition

• Order Statistics
• Sufficient Statistic
  • Complete Sufficient Statistic