Statistic

Summary

• Given a sample \(x_1,…,x_n\) and a function \(g:R^n→R\) then

\[z=g\left( x_1,…,x_n \right)\]

• is called a statistic .

Examples

• The sample mean

\[\bar{x}= \frac{1}{n}\sum_{i=1}^{n}{ x_i }\]

• The sample variance

\[s_x^2= \frac{1}{n-1}\sum_{i=1}^{n}{ {\left( x_i-\bar{x} \right)}^2 }\]

• The sample covariance

\[s_{x,y}^2= \frac{1}{n-1}\sum_{i=1}^{n}{ \left( x_i-\bar{x} \right)\left( y_i-\bar{y} \right) }\]