October 2018
Beginner
250 pages
12h 14m
English
In this chapter, a key extra assumption is added to the classical regression model (CRM) specified in Section 7.2. Like the CRM itself, this is not necessarily a realistic assumption as it stands, but it often holds as an approximation and yields powerful results – not less than a complete theory of statistical inference. The Gaussian classical regression model (GCRM) shares assumptions GCRM(i)–(iii) with CRM(i)–(iii) and adds the following
Assumption GCRM(iv): 
means that the disturbances are jointly normally distributed, with density function

If
is any fixed conformable matrix and
a fixed conformable vector, GCRM(iv) and the linearity property of the normal distribution implies that

In particular, since by (7.2) and (7.1)
and
it follows ...