Advanced statistics books recommendation 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.


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*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)

 A: Not sure if these are at the level you're looking for, but some books I've found useful-
GLMs - McCullagh and Nelder is the canonical book
PCA - A User's Guide to Principal Components - despite the title it does go into some degree of depth on the topic
A: I really like Larry Wasserman's books "All of Statistics" and "All of Nonparametric Statistics". They are very readable, and cover a lot of ground quickly.
A: The Nonlinear Models books that I like and rely on are (1) Bates and Watts and (2) Gallant.  Both are published by Wiley.  
A: For Bayesian analysis (including imprecise analysis), I'm going to put in big plugs for:


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*Bernardo, J.M. and Smith, A.F.M. (2000) Bayesian Theory. Wiley: Chichester.

*Gelman, A. et al (2013) Bayesian Data Analysis (Third Edition). CRC Press: Boca Raton. 

*Walley, P. (1990) Statistical Reasoning with Imprecise Probabilities. Chapman and Hall. 
That last book, by the brilliant Peter Walley, is an eye-opener on different ways of doing sensitivity analysis, and the fact that this can be built into probability theory at an axiomatic level.
A: Mehta (2014) Statistical Topics (ISBN: 978-1499273533) is good intermediate level statistics story telling.  Doesn't cover much of you topics you noted above though.
A: 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.
A: Some books on Likelihood Estimation

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** Amari, Barndorff-Nielsen, Kass, Lauritzen and Rao, Differential geometry in statistical inference.
$-\small{\text{Geometrical approach for proving existence, uniqueness and other properties of MLE.}}$


** Butler, Saddlepoint Approximations with Applications.
$-\small{\text{Saddlepoint approximations to the MLE on complicated models.}}$


** Cox, Principles of Statistical Inference.
$-\small{\text{A basic reference on MLE.}}$


** Cox and Barndorff-Nielsen, Inference and Asymptotics.
$-\small{\text{Likelihood, pseudo-likelihood, approximation theorems and asymptotics explained by}}$
$ \small{\text{two exponents in this area.}}$


** Edwards, Likelihood.
$-\small{\text{A reference for a general discussion on this concept.}}$


** Ferguson, A Course in Large Sample Theory.
$-\small{\text{Contains classical results on asymptotic properties of point estimators.}}$


** Kalbfleisch, Probability and Statistical Inference II. $\spadesuit$
$-\small{\text{Introductory book containing interesting basic results such as the continuous }}$
$\small{\text{approximation to the likelihood which is not always explained.}}$


** Lehmann and Casella, Theory of Point Estimation.
$-\small{\text{Classical results on point estimation, an essential reference.}}$


** Pace and Salvan, Principles of Statistical Inference: From a Neo-Fisherian Perspective.
$-\small{\text{A good reference on a school of thought becoming more and more popular:}}$
$\small{\text{the Neo-Fisherian.}}$


** Pawittan, In All Likelihood: Statistical Modelling and Inference Using Likelihood.


** Serfling, Approximation Theorems of Mathematical Statistics.
$-\small{\text{More rigorous book, here you can find the mystical "regularity conditions".}}$


** Severini, Likelihood Methods in Statistics.


** Shao, Mathematical Statistics.
$-\small{\text{Classical results, good as a textbook.}}$


** Sprott, Statistical Inference in Science. $\spadesuit$
$-\small{\text{Basic reference on likelihood, profile likelihood and classical statistical modelling.}}$


** van der Vaart, Asymptotic Statistics.
$-\small{\text{A general reference on: modes of convergence, properties of MLE, delta method,}}$
$\small{\text{ moment estimators, efficiency and tests.}}$


** Young and Smith, Essentials of Statistical Inference.
$-\small{\text{A more recent book on: Likelihood, pseudolikelihood, saddlepoint approximations,}}$
$\small{p^*\text{ formula, modified profile likelihoods and more.}}$
$\spadesuit$ Suggestion for the OP
A: My guess is that, for your requirements, the best book on generalized linear models is probably:  


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*Agresti's Introduction to Categorical Data Analysis
There are other books that might be considered better, but I suspect would be less appealing to a practitioner who would prefer to avoid dense mathematics:  


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*Agresti's Categorical Data Analysis (his primary text),
is good for practitioners, but is denser  

*McCullagh & Nelder's Generalized Linear Models,
is, I hear (I've never tried it), the bible for this, but demands considerable mathematical sophistication  

*Dobson's Introduction to Generalized Linear Models,
is possible to get through, but still pretty mathematically dense, IMO  


As for your other topics, I'm afraid I don't know of books for them, but maybe others can make some recommendations.
A: One really simple introductory statistics book is Andy Field's "Discovering Statistics using R" - also available for SPSS.
It contains a lot of nice examples and is even fun to read. Less precise, though compared to other books, but with very little mathematical formulations and lots of text. I found it easy for a basic start, and am still using it from time to time.
