# Reddit reviews Mathematical Statistics with Applications

We found 14 Reddit comments about Mathematical Statistics with Applications. Here are the top ones, ranked by their Reddit score.

We found 14 Reddit comments about Mathematical Statistics with Applications. Here are the top ones, ranked by their Reddit score.

## 14 Reddit comments about Mathematical Statistics with Applications:

I've wasted too much time trying to find the so-called "right" statistics book. I'm still early in my journey, going through calculus using Prof. Leonards videos while working through a Linear Algebra book all in prep for tackling a stats book. Here's a list of books that I've had a look at so far.

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These seem to be of a similar level with regards to rigour, as they aren't that rigourous. That's not to say you can get by without the calculus prereq and even linear algebra

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The other two I've been looking at which seem to be a lot more complex are

And then there's Casella and Berger's Statistical inference, which I looked at once and decided not to look at again until I can manage at least one of the aforementioned books. I think I'm leaning most to the first book listed. Whichever one you decide to use, good luck with your journey.

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Since you are already going to take Machine Learning and want to build a good statistical foundation, I highly recommend Mathematical Statistics with Applications by Wackerly et al.

If you are really good at calculus, learn some probability first. My personal favorite is Wackerly et al.'s

Mathematical Statistics with Applications. This covers both the probability and mathematical stats background that you will see in college. The book is quite pricey, so I recommend buying it on half (dot) com.You might notice that this text has a lot of negative reviews. This review of the above text explains the prerequisites quite well - this is not an AP-stats type of textbook:

> I believe that this book is designed to teach statistics to those who plan on actually using it professionally (and not just to pass a required course) while continuing to develop one's own mathematical maturity. While Wackerly is not as rigorous as Ross's Probability book, it is taught at a completely different level than a non-calculus-based statistics course that are often taken by students who simply want to know which formula to use for the exam. I think of it as the ideal text for anyone in the sciences, engineering, or economics. The level of rigor is similar to the 2 Calculus courses online at MIT-Open Course Ware.

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> this book derives virtually every formula, allowing students to continue to develop their mathematical maturity which will be required for higher-level courses on bootstrapping, pattern recognition, statistical learning, etc. In order to follow these proofs (and also in order to solve problems from about 4 chapters) one must have a firm grasp of calculus. That not only means that one can integrate, differentiate, work with series, use L-Hopital's rule and integration-by-parts, but also that one understands the concepts of calculus very well.

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> The proofs are all broken down so as to not really skip many steps, but as someone away from math for over 25 years, I must write down each step myself and make sure that I understand it before moving on. If a few steps are skipped, I must connect the dots myself using plenty of scratch paper. My math background was the Calculus series, ordinary differential equations, and linear algebra. About 1/5 of all problems are proof-based.

See also this review:

> I will concede that you can't come at this book without an understanding of at least integral calculus (and since so many people get turned off by Algebra, well...), so I suspect a lot of the negative reviews here are written by people who jumped in the deep end of the pool without having a few swimming lessons. If you know the calculus and basic set theory, the book is exceedingly easy to follow.

Some of what you learned in AP Stats will transfer to calculus-based statistics, but a lot of what you learn in your undergrad will not be like anything you learned in AP Stats. Hence I'm recommending that you start from scratch on probability.

Generally speaking, I agree with /u/Akillees89 that you should get a head start in developing your math background. However, I don't agree that Strang or Axler are good for linear algebra for statistics. See my post here.

I learned from Wackerly which is decent, though I think Devore's presentation is better, but not as deep. Both have plenty of exercises to work with.

Casella and Berger is the modern classic, which is pretty much standard in most graduate stats programs, and I've heard good things about Stat Labs, which uses hands-on projects to illuminate the topics.

> I'd like to know, how did you learn to use R?

My batshit crazy lovable thesis advisor was teaching intro datascience in R.

He can't really lecture and he have high expectation. The class was for everybody including people that don't know how to program. The class book was advance R http://adv-r.had.co.nz/... (red flag).

We only survived this class because I had a cs undergrad background and I gave the class a crash course once. Our whole class was more about how to implement his version of random forest.

I learned R because we had to implement a version of Random forest with Rpart package and then create a package for it.

Before this a dabble in R for summer research. It was mostly cleaning data.

So my advice would be to have a project and use R.

>how did you learn statistics?

Master program using the wackerly book and chegg/slader. (https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817)

It's a real grind. You need to learn probability first before even going into stat. Wackerly was the only real book that break down the 3 possible transformations (pdf,cdf, mgf).

I personally think you should brush up on frequentist statistics as well as linear models before heading to Bayesian Statistics. A list of recommendations directed at your background:

I would try

Mathematical Statistics and Data Analysisby Rice. The standard intro text for Mathematical Statistics (this is where you get the proofs) is Wackerly, Mendenhall, and Schaeffer but I find this book to be a bit too dry and theoretical (and I'm in math). Calculus is less important than a thorough understanding of how random variables work. Rice has a couple of pretty good chapters on this, but it will require some mathematical maturity to read this book. Good luck!This book comes to mind.

This was mine.

Just completed Probability this semester, and moving on to Statistical Inference next semester. Calc. B is a prerequisite, and wound up seeing plenty of it along with a little Calc C (just double integrals). I'm an Applied Mathematics undergrad major btw and former Physics major from some years ago. I wound up enjoying it despite my bad attitude in the beginning. I keep hearing from fellow math majors that Statistical Inference is really difficult. Funny thing is I heard the same about Linear Algebra and didn't find it overwhelming. I'll shall soon find out. We used Wackerly's Mathematical Statistics with Applications. I liked the book more than most in my class. Some thought it was overly complicated and didn't explain the content well. Seems I'm always hearing some kind of complaint about textbooks every semester. Good luck.

Sadly the only university in my city lost their accreditation since they couldn't pay a competitive salary.

I lucked out because my Statistics professor is insanely qualified. (Ph.D in Mathematics and Ph.D in Statistics) So our Stats course covers MGFs and the derivations of all the theorems. Pretty much every question in this book: http://www.amazon.ca/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

Thanks a lot for the response. The thought of taking on something of this magnitude with no real life mentor-ship is really daunting.

If you want to do statistics in a rigorous way you should start with calculus and linear algebra.

For calculus I recommend Paul's notes -> http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

They are really clearly written with good examples and provide good intuition.

As supplement go through 3blue1borwn Essence of calculus. I think it's an excellent resource for providing the right intuition.

For linear algebra - linear algebra - Linear algebra done right as already recommended. Additionally, again 3blue1brown series on linear algebra are top notch addition for providing visual intuition and understanding for what is going on and what it's all about.

Finally, for statistics - I would recommend starting with probability calculus - that way you'll be able to do mathematical statistics and will have a solid understanding of what is going on. Mathematical statistics with applications is self-contained with probability calculus included. https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

If you want to go deep, try a math stats book. Although there would probably be disagreement in this subreddit on which is the best, they are all pretty much the same. Maybe try an early edition of the Wackerly book (I think that one is most widely used one). A lot of people would suggest Casella and Berger, but I would suspect those people have never taught a course and forget that that book does require a bit of mathematical maturity. Go with an undergrad book.

For R, I would suggest either going through a tutorial (such as the swirl package), or, what I am assuming how most people learned it, buying an applied stats book and just doing the problems in R. You have to go through the hump of learning it, but you learn programming by doing it. After you are done with math stats, a good next step in the applied direction is Regression and ANOVA/Design. Regression, there are a ton of books. But again, the first few chapters of most books are the same. I would try and find a cheapo book with a modern typeset. ANOVA... probably want to go with Montgomery. I don't know the others too well though.

Probability and Random Processes by Grimmett is a good introduction to probability.

Mathematical Statistics by Wackerly is a comprehensive introduction to basic statistics.

Probability and Statistical Inference by Nitis goes into the statistical theory from heavier probability background.

The first two are fairly basic and the last is more involved but probably contains very few applied techniques.