Overview
For this page, we assume that we have a dataset representing sample points from a distribution of a random vector of values {% X_1,X_2,...,X_n %} see Lai/Xing pg 29
Sample Mean
The sample mean for a set of vectors has the same formula as for non-vector quantities.
{% \bar{X} = \frac{1}{n} \sum X_i %}
Sample Covariance
The sample covariance has a particularly simple format when the matrix transpose is used.
{% S = \frac{1}{n-1} \sum (X_i - \bar{X})(X_i - \bar{X})^T %}