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

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