A Non-Least Squares Approach to Linear Models

This book provides a unifying framework which can be used to apply many types of linear models used in applications to the analysis of data generated by scientific experiments. While other texts on linear models use least squares as the basis for developing linear estimation theory, this book uses a non-least squares approach for developing the same theory. The benefits of the approach used here are that it allows for the initial consideration of more complex models and it simplifies the proofs of many of the main results given, thus making the book easier to read. In addition, through the use of a concept called “correspondence”, the text provides the first formal systematic approach for exploring relationships between different representations for models used to describe the same expectation space assumed for a given data set.