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An Introduction to Econometric Theory
book

An Introduction to Econometric Theory

by James Davidson
October 2018
Beginner content levelBeginner
250 pages
12h 14m
English
Wiley
Content preview from An Introduction to Econometric Theory

10The Gaussian Regression Model

10.1 Testing Hypotheses

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): images

images means that the disturbances are jointly normally distributed, with density function

images

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

images

In particular, since by (7.2) and (7.1)

and

it follows ...

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