In this module, we will discuss how to find the most precise and accurate estimate in linear models. An introduction to the concept of Best Linear Unbiased Estimation (BLUE), its theory and implication, and its relation to other estimators such as WLSE, maximum likelihood, and minimum variance estimators, will be provided. The concept of BLUE and its application in some problems will be demonstrated by examples and exercises.

By the end of the week you will be able to:

•  explain the concept of Best Linear Unbiased Estimation and its properties,
•  apply BLUE for real-life examples and interpret the solution.

Note: Least squares estimation is a deterministic concept. That is, it does not account for the stochastic properties of the observations in the criterion to choose the best model.  But BLUE explicitly considers the fact that observations are stochastic variables.

Optional part: Non-linear least squares

The last part of this module is optional – it is about the application of least squares for non-linear functional models. In this course, the main focus is on problems with a linear functional model. However, in practice for many estimation problems the observation equations are non-linear. In this optional part, we will show how you can solve problems with a non-linear functional model based on the principle of non-linear least squares.