• maximum likelihood estimation
• R
• econometrics
• heteroskedasticity

This thesis consists of five chapters.

Chapter 1 briefly introduces the framework from which this work starts, that is the Standard Linear Model and its underlying assumptions. The classical OLS estimator is reviewed, together with its finite-sample and asymptotic properties. Finally, we analyse the case in which the assumption of homoskedastic errors is violated, describing the consequences of such violation on the properties of OLS estimator.

Chapter 2 presents two of the most common tests used to deetect heteroskedasticity. Moreover, it examines two methods used to deal with non-constant error variance. The first method is based on heteroskedastic-robust estimators, that allow to adjust the estimator of OLS-based covariance matrix. The second method is Generalised Least Squares, which is more efficient than OLS if the spherical errors assumption is not satisfied, but requires prior knowledge of the covariance matrix. When this is not the case, Feasible Generalised Least Squares can be used.

Chapter 3 considers a framework to deal with heteroskedasticity using Maximum Likelihood estimation. Mathematical aspects and analytical results have been discussed.

Chapter 4 explores the functionalities of a new R package "lmH" created to implement the framework presented in chapter 3. The main function, also named "lmH", performs Maximum Likelihood estimation, and has the same structure as the classical "lm" function for standard linear models. Moreover, the package includes all the main functions used by "lm" for summary and prediction. All the necessary R code is reported in the appendix.

Finally, chapter 5 deals with some real data suffering from heteroskedasticity. The "lmH" package is applied and the results are compared with the standard linear model.