Chapter 4 Assumptions on the regressors

The computation and all the statistical properties of the estimators obtained in the previous chapter are based on the standard assumptions 3.5. However, It is rare when all these assumptions are satisfied. In most cases, one or more than one assumption can be violated, and hence the estimators should be recomputed or adjusted to save the required statistical properties. Also, statistic tests may not conserve their distributions determined before.

In this chapter, we will investigate each hypothesis separately when it is possible, because it may exist some dependence between assumptions such as the dependence between the assumption of linearity and the constancy.