Rigorous text on statistics

In summary, the person is looking for a mathematically rigorous text on statistics and probability. They have a background in linear and abstract algebra and calculus and analysis. They do not want a text that is not rigorous in its proofs. Suggestions for a starting book include Data Analysis - A Bayesian Tutorial and books by Lehmann. They also recommend going to a library to see what works best for the individual.
  • #1
776
2
Hi PF, looking for a recommendation on a mathematically rigorous text on statistics (and perhaps probability). I have a decent amount of knowledge on linear & abstract algebra and calculus and analysis, so I don't mind if it uses them. What I don't want is a text that fails to prove its theorems with rigor. Suggestions are appreciated, thanks!

BiP
 
Physics news on Phys.org
  • #2
I've done some looking but from what I've seen, books on statistics tend to be pricey and each looks different from the rest. So perhaps it is better to start with a book that is rigorous-looking but practical also, just to get a road map view of things.

Data Analysis - A Bayesian Tutorial might be a good way to start.

After reading this you would hopefully know where your interest lies and could guide yourself to further reading. And it would be useful to know where things fit in. Ultimately, your knowledge of statistics will be organized around how it is used. Use the "look inside" to see if this would be worthwhile.

I can't recommend a completely rigorous book because this subject is so confusing to me.

PS. Here is a cheaper book that claims to be mathematical and rigorous but I can't say if it is good or if it is what you should be learning.
 
Last edited:
  • #3
Since you haven't had a lot of replies, here is my two cents (from an engineer who uses staistical inference a fair amount but is *not* interested in all the rigor!)

The books by Lehmann seem to be the ones referenced all the time:
https://www.amazon.com/dp/0387988645/?tag=pfamazon01-20
https://www.amazon.com/dp/0387985026/?tag=pfamazon01-20

other books the stats people seem to like:
https://www.amazon.com/dp/0534243126/?tag=pfamazon01-20
(I own the first edition of this one, which has plenty of proofs but doesn't motivate the statistics very well to someone like me! This is the easiest of all the books I list here)

Another:
https://www.amazon.com/dp/0132306379/?tag=pfamazon01-20

Then there is the 60+ year old classic:
https://www.amazon.com/dp/0691005478/?tag=pfamazon01-20

If I were you I would go to your library and see what works for you. Don't buy any of these without looking at them first. Only YOU know what you are looking for.

best regards,

jason
 

1. What is the purpose of a rigorous text on statistics?

A rigorous text on statistics is designed to provide a comprehensive and in-depth understanding of statistical concepts and methods. It aims to develop critical thinking skills and the ability to analyze and interpret data accurately.

2. Who can benefit from studying a rigorous text on statistics?

Anyone interested in understanding the fundamentals of statistics and its practical applications can benefit from studying a rigorous text on statistics. This includes students, researchers, and professionals in various fields such as science, business, and social sciences.

3. What topics are typically covered in a rigorous text on statistics?

A rigorous text on statistics usually covers topics such as descriptive statistics, probability theory, hypothesis testing, regression analysis, and experimental design. It may also include advanced topics such as multivariate analysis and time series analysis.

4. How can a rigorous text on statistics be useful in real-world situations?

A rigorous text on statistics provides a strong foundation for understanding and analyzing data in various real-world situations. It can help individuals make informed decisions, solve problems, and draw accurate conclusions based on data.

5. Are there any prerequisites for studying a rigorous text on statistics?

While a basic understanding of mathematics and algebra is helpful, most rigorous texts on statistics do not require any prior knowledge of statistics. However, some may assume familiarity with certain mathematical concepts such as derivatives and integrals.

Suggested for: Rigorous text on statistics

Replies
10
Views
1K
Replies
12
Views
975
Replies
2
Views
618
Replies
2
Views
1K
Replies
56
Views
7K
Replies
2
Views
454
Replies
12
Views
967
Replies
4
Views
919
Replies
1
Views
548
Replies
12
Views
5K
Back
Top