Coming up with a short list of my favorite books in statistics was more challenging than I had expected. There are so many fantastic books in the field (and as you may be aware, the field is so vast). I factored depth, level of mathematics level, and relevancy in my consideration. Of course, these factors were mostly subjective.
As of today, these are my top 5 books (no particular order):
An Introduction to Statistical Learning (ISLR)
When I first started studying statistics, I was introduced to this book and I thought it was god sent (it’s still freely available so there is absolutely no risk!). The authors cover variety of topics such as classical linear regression, classification, resampling methods, survival analysis, and multiple testing. I think the level is very appropriate for an upper-class undergraduate student. And they have included [working] R-code!
Even if you don’t fully understand it, you can at least run the code.
Computational Statistics
Computational statistics is a tool set that all statisticians should have in their tool box. I think a good place to start learning about the topic is this comprehensive book. Although it was written few years ago, I think many of the topics covered are still relevant today.
The authors cover topics on EM, Monte Carlo simulation, optimization, bootstrapping, and density estimation. Obviously, I would like to see more modern topics.
I think the appropriate level of this book is again an upper-class undergraduate student and first-year graduate students.
Probability for Statisticians
There are so many excellent probability textbooks such by A Probability Path by Resnick, Probability: Theory and Examples by Durrett, and Probability and Measure by Billingsley to just name a few. I wish I can list all but I have elected to narrow it to one book.
The reason I chose this book was I noticed a pattern. I noticed that when I wanted clarification on a definition or a concept, I would go to this book as my first option before reading others. I think the main reason is that this book is better tailored for statisticians while others are written for mathematicians.
Other textbooks are also great (many of them have awesome exercises and problem sets). The advantage of this book over others is slight at best.
Mathematical Statistics
Although this wasn’t one of the textbooks that was formally used in my program, I love this book for its clarity. Having said that, this is definitely a graduate level textbook (mostly for PhD students) with working knowledge of measure theory and background is statistics.
I think an honorable mention in mathematical statistics is Statistical Inference by Casella & Berger. It is an easier read (advanced undergraduate or first-year graduate student) than the book by Shao. Background in measure theory is not necessary.
However, I find the book by Casella & Berger to be not very rigorous and at times little sloppy. On the positive note, Statistical Inference has many exercises and problem sets. This may suit better for someone who want to self-study.
The Bayesian Choice
To be fully transparent, I am not a Bayesian. I have not read many Introduction Bayesian books, but I have read books such as Bayesian Data Analysis by Gelman, et al. and Statistical Rethinking by McElreath.
However, I wanted to include a Bayesian book in this list. One of the best books I read on this topic is this book by Christian Robert. I enjoyed his approach to Bayesian as decision theory. I thought the development of the material was clearer than that of Gelman’s book (I know — how can I make such a claim!)
Bayesian Choice is written for advanced undergraduate and graduate students. I especially enjoyed the numerous exercises and problem sets.
When making such a list, there are so many factors to consider such as intended audience. For example, I would not recommend these books to beginners in statistics. And I may want to segment by topic in statistics. Nevertheless, it was fun making this list.
Thank you for taking time to read! If you have any comments or other recommendations, please feel free to share.
