I took several statistics courses in college but I found that my education was very theory driven.
I was wondering if any of you had a text in Applied Statistics (at the graduate level) that you recommend or have had good experience with.
Solved – Do you have recommendations for books to self-teach Applied Statistics at the graduate level
applicationexperiment-designmodelingreferencesregression
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I would recommend two books if you are interested in smoothing techniques, especially in density estimation and regression (rather than in tests that don’t require classical normality assumptions, which are often based on ranks rather than the raw data):
- Nonparametric and Semiparametric Models by Härdle, Müller, Sperlich, and Werwatz
- Li and Racine's Nonparametric Econometrics: Theory and Practice
The first is much slimmer, a bit more introductory, with lots of examples and illustrations. It covers histograms, nonparametric density estimation, nonparametric regression, semiparametric and generalized regression models, single index models, generalized partial linear models, additive models and their marginal effects and generalized additive models.
The second tome covers nonparametric kernel methods, semiparametric methods, consistent model specification tests, nonparametric nearest neighbor and series methods, and some time series, simultaneous equations, and panel data models at the end. There is not too much about QR in this book. Koenker's QR would make a nice supplement.
It is also worth mentioning some other books. While comprehensive and worth reading later, I found Pagan and Ullah to be a difficult first introductions to this material. I have heard good things about Yatchew's Semiparametric Regression book, but I have not read it myself.
On the grounds that you want something (a) well-motivated, (b) less dense, and (c) introductory (undergraduate or early graduate level), you might want to consider a text like "Mathematical statistics and its applications" by Larsen and Marx. The "and its applications" is important because the authors give a practical motivation to the theory that you may have found missing in Casella and Berger. This is still a "mathematical statistics" book though, not an applied practitioner's guide on how to apply statistical methods that are otherwise treated as a "black box". There are exercises in Minitab, which I am sure you could translate into another statistical language of your choice.
It only covers a small fraction of what C&B do, and it may not be "pure" enough for your tastes; perhaps you will find the applications a sort of contamination rather than motivation! But C&B is quite a heavy book to hit, if it's the first that you take on. Larsen and Marx is (in my opinion) quite clearly written, covers simpler material, and is very well type-set. That all should make it easier to get through. Perhaps after working through a book pitched at this level, it would be easier to mount a second assault on C&B or similar.
The reviews on amazon are pretty mixed; it's interesting that people who taught courses using the book were generally pretty favorable (one criticism is that it is not as mathematically rigorous as it might have been) while students on courses where the book was a set text were more negative.
If you would prefer a text that was more mathematical in nature, then I think you might need to work on your background knowledge first. I can't see how it is possible to understand a rigorous proof of the Central Limit Theorem without a good background in analysis, for instance. There are some "intermediate" texts, of which Larsen and Marx is one, which are not so rigorous as to be incomprehensible to someone without an analysis background (so you get a "sketch proof" of the CLT rather than a formal one, for example), but which are still "mathematical statistics" rather than "applied statistics". I suspect your basic choice lies between the more mathematical approach, or reaching into statistics via this sort of intermediate-level book. But if you want to take things higher, then at some point you are going to need some more mathematics.
MIT runs a course for introductory statistics for (undergraduate) economics, with a set text of "Probability and Statistics for Engineers and Scientists" by Sheldon Ross, and recommended texts of Larsen and Marx or alternatively DeGroot and Schervish, "Probability and Statistics". The MIT course authors compare them as:
Larsen and Marx's book is a bit more chatty than Ross', while DeGroot and Schervish's is a very good book but somewhat more difficult
If you want something antithetical to the dry style of C&B then the chattier style of L&M might suit you. But those other suggestions for texts of a similar difficulty level might also interest you.
Best Answer
Some very good books: "Statistics for Experimenters: Design, Innovation, and Discovery , 2nd Edition" by Box, Hunter & Hunter. This is formally an introductory text (more for chemistry & engineering people) but extremely good on the applied side.
"Data Analysis Using Regression and Multilevel/Hierarchical Models" by Andrew Gelman & Jennifer Hill. Very good on application of regression modelling.
"The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition" (Springer Series in Statistics) 2nd (2009) Corrected Edition by Hastie Trevor, Tibshirani Robert & Friedman Jerome. More theoretical than the two first in my list, but also extremely good on the whys and ifs of applications. -- PDF Released Version
"An Introduction to Statistical Learning" (Springer Series in Statistics) 6th (2015) by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani -- PDF Released Version
Working your way through these three books should give a very good basis for applications.