There are several threads on this site for book recommendations on introductory statistics and machine learning but I am looking for a text on advanced statistics including, in order of priority: maximum likelihood, generalized linear models, principal component analysis, non-linear models. I've tried Statistical Models by A.C. Davison but frankly I had to put it down after 2 chapters. The text is encyclopedic in its coverage and mathematical treats but, as a practitioner, I like to approach subjects by understanding the intuition first, and then delve into the mathematical background.
These are some texts that I consider outstanding for their pedagogical value. I would like to find an equivalent for the more advanced subjects I mentioned.
- Statistics, D. Freedman, R. Pisani, R. Purves.
- Forecasting: Methods and Applications, R. Hyndman et al.
- Multiple Regression and Beyond, T. Z. Keith
- Applying Contemporary Statistical Techniques, Rand R. Wilcox
- An Introduction to Statistical Learning with Applications in R – (PDF Released Version), Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani
- The Elements of Statistical Learning:Data Mining, Inference, and Prediction. – (PDF Released Version), Hastie, Tibshirani and Friedman (2009)
Best Answer
Maximum likelihood: In all Likelihood (Pawitan). Moderately clear book and the most clear (IMO) with respect to books dealing with likelihood only. Also has R code.
GLMs: Categorical Data Analysis (Agresti, 2002) is one of the best written stat books I have read (also has R code available). This text will also help with maximum likelihood. The third edition is coming out in a few months.
Second on my list for the above two is Collett's Modelling Binary Data.
PCA: I find Rencher's writing clear in Methods of multivariate analysis. This is a graduate level text, but it is introductory.