Advanced Linear Models for Data Science
This book is 50% complete
Last updated on 2017-01-06
About the Book
This book is about 50% finished. It is only available in pdf form.
Linear models are the cornerstone of statistical methodology. Perhaps more than any other tool, advanced students of statistics, biostatistics, machine learning, data science, econometrics, etcetera should spend time learning the finer grain details of this subject.
In this book, we give a brief, but rigorous treatment of advanced linear models. It is advanced in the sense that it is of level that an introductory PhD student in statistics or biostatistics would see. The material in this book is standard knowledge for any PhD in statistics or biostatistics.
Students will need a fair amount of mathematical prerequisites before trying to undertake this class. First, is multivariate calculus and linear algebra. Especially linear algebra, since much of the early parts of linear models are direct applications of linear algebra results applied in a statistical context.In addition, some basic proof based mathematics is necessary to follow the proofs. In addition, some regression models and mathematical statistics are needed.
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Table of Contents
- Introduction
- Background
- Single parameters
- Linear regression
- Least Squares
- Examples
- Bases
- Residuals
- Expectations
- Normal distribution
- Distributional results
- Residuals and diagnostics
- Under and overfitting
- Penalties
- Asymptotics
- Mixed models
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