Overview
Large Sample Properties
Without making any assumptions about the distribution of {% \epsilon %}, it is impossible to derive distributions for {% \beta %} and {% \sigma %}. However if the sample size is considered to be large, then the central limit theorem can be marshalled to derive asymptotic estimates of the distributions.Under these assumptions, it can be shown that
{% \hat{\beta} - \beta \rightarrow N(0, \sigma ^2 (X^T X)^{-1}) %}