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This is my first post here. In a very short way I was asking for prob/stat books that are very rigorous (again, this means axioms, theorems ,proof). User whuber closed my question as a duplicate of this question. Now the other question is just asking for statistics books for non-statistician scientists. It does not require mathematical rigor as a condition. My question does. Thus, they are not duplicates. Because all answers that I see in the question that whuber thought was a duplicate of mine are either useless or answers that I am not able to judge if they would be answers to my own question.

I will copy few sentences from some answers in the question that whuber marked as a duplicate:

"with concise and accurate language, but without too much mathematics"

"A lot of Social Science / Psychology students with minimal mathematical background like Andy Field's book: Discovering Statistics Using SPSS. "

I request that my question is opened again.

Thanks for your time.

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  • $\begingroup$ I support this. In fact in conversation with @Andre Silva, now deleted, I made the point that Amr was seeking a rigorous book, at the opposite end from e.g. Andy Field's books. $\endgroup$ – Nick Cox Aug 29 '13 at 10:09
  • $\begingroup$ @NnickCox Thanks a lot. If you have any suggestions on an appropriate book for me, I would like to hear them as well. $\endgroup$ – Amr Aug 29 '13 at 11:22
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    $\begingroup$ Sorry, but my personal view is that starting from scratch and being rigorous don't mix. I think you need to know what you can do before you learn how to be rigorous about it, to paraphrase something John Tukey once said. But I am very happy to let your question be posed to consenting adults. $\endgroup$ – Nick Cox Aug 29 '13 at 11:41
  • $\begingroup$ @NickCox Why not? For example any undergrad analysis books start by stating the field axioms or by constructing the real numbers (this means starting from scratch for me) yet they are rigorous. $\endgroup$ – Amr Aug 29 '13 at 12:43
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    $\begingroup$ I should have said in statistics, but I still stand by what I said. Your analogy doesn't convince: a first book in more rigorous analysis is still building on years of elementary and high/secondary school education and experience with algebra (and usually calculus). What can be difficult for mathematical types to understand is that statistics is an art in approximation with real data, with tricks and devices, and not just a deductively-derived branch of mathematics. (A more direct answer is simply that I don't know that anyone has tried to do exactly what you want.) $\endgroup$ – Nick Cox Aug 29 '13 at 12:53
  • $\begingroup$ @NickCox Thanks for your help. I just have a few remarks: I was not making an analogy, but instead I wanted to disprove the statement:"All math books that are rigorous do not start from scratch" by giving a counterexample. Another thing, I think it would have been fine with me if I only studied analysis without calculus, in that sense I think calculus was a waste of time for me. $\endgroup$ – Amr Aug 29 '13 at 13:12
  • $\begingroup$ @NickCox So if you have a stat book that starts from scratch (in the sense that it puts all axioms and definitions from the beginning just like analysis book would do), I would like to know it. I think it would be a good book for me to study even if I have not learnt the "Calculus equivalent" of statistics first. I think (hopefully) that I am mathematically-mature enough to handle it. $\endgroup$ – Amr Aug 29 '13 at 13:12
  • $\begingroup$ @NickCox The most important part of your comment in my opinion is when you said: "and not just a deductively-derived branch of mathematics". Do you mean that mathematical statistics has some sort of an abductive character. See: en.wikipedia.org/wiki/Abductive_reasoning $\endgroup$ – Amr Aug 29 '13 at 13:13
  • $\begingroup$ OK. This is an enjoyable conversation for me, but better truncated. My first introduction to calculus was inspirational, and I enjoyed Latin too, so there you go. $\endgroup$ – Nick Cox Aug 29 '13 at 13:14
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    $\begingroup$ It might help to narrow the scope of your question a bit - a mathematically rigorous approach to hypothesis testing, generalized linear models, optimal experimental designs, robust non-parametric methods... ? - I can think of books that treat any one of these rigorously, but not a single book that does so for all of Statistics. (And I second Nick's point: even if you weren't trying to learn to apply statistics, it's usual to have covered many topics in a shallower, more heuristic, fashion before studying a few of them deeply.) $\endgroup$ – Scortchi - Reinstate Monica Aug 29 '13 at 13:20
  • $\begingroup$ @Scortchi I was thinking of this book : amazon.com/dp/0387945466/?tag=stackoverfl08-20 I am not sure if it starts from scratch though as I am not able to look inside it. Do you have any idea if it starts from scratch $\endgroup$ – Amr Aug 29 '13 at 13:31
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    $\begingroup$ Then perhaps this question is closer to yours. IMO all the answers might suit you except Wasserman (though I've not read Schervish). $\endgroup$ – Scortchi - Reinstate Monica Aug 29 '13 at 13:39
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    $\begingroup$ I think most of these could be said to start from scratch in a sense, but I wouldn't have understood a single page of any before I'd spent a few years studying/applying more elementary statistics. Everyone's different - just warning you. $\endgroup$ – Scortchi - Reinstate Monica Aug 29 '13 at 13:53
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    $\begingroup$ I like this book. We used a pre-print version of this for my theoretical statistics sequence in grad school. It is self contained but does pre-suppose basic knowledge of linear algebra and calculus. It reviews the key pieces of measure theory needed for the subsequent chapters. I like this book because it covers everything you need to know but still leaves room for ingenuity on the part of the reader. If you work through this book you will come away with a strong foundation in theoretical statistics. $\endgroup$ – Macro Aug 29 '13 at 14:41
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    $\begingroup$ I have edited the original question to reflect my understanding that it seeks theoretical, mathematical texts. My current belief is that this does not duplicate existing threads and so I have reopened it. (If a duplicate does come to light, one of them would likely be closed or merged.) $\endgroup$ – whuber Aug 29 '13 at 15:21
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My concern about the thread in question is that by allowing apparently minor variations (such as "rigorous" versus "for scientists," which arguably already implies some form of rigor) of marginal questions (such as requests for lists of books) we will accumulate a series of confusingly similar threads that, because of their proliferation, serve nobody well. I simply ask anyone who is considering posting a request for a list of books/resources/references that they first research similar questions on this site and carefully consider whether their needs are so different that a genuinely new list is needed. I also ask the community in its voting to favor fewer, rather than more, such threads on this site.


Background

Normally requests to reopen questions should appear in comments to the question, where they will be addressed (in good time) by moderators and high-reputation community members. Because of the unusual appearance of a request here in meta, I feel obliged to provide some background information about the circumstances.

In comments to the original question, user @whuber requested an explanation of how the answers to the apparent duplicate question were insufficient. OP's reaction was a series of increasingly loud comments culminating in challenging @whuber's understanding, followed by posting the present question here on meta. This is known as an ad hominem attack: it is inappropriate anywhere on StackExchange (and anywhere else civil discourse is valued) because it improperly shifts attention from the discourse to the discussants.

In the present instance this is not a problem, because @whuber is a moderator and part of that job is putting up with the bad as well as the good. I would like to take this opportunity, though, to direct the OP's attention to the "Be Nice" section of the site policy on behavior. My request is that all users, even avowedly new ones, review this material and strive to comply with it.

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  • $\begingroup$ Only with time we can get experience in the community. @amr is a experienced 10k user on mathematics.se and I am risking to say he had bad luck posting his first thread here on a (let's say) polemic issue and maybe got a little disapointement to have a question closed. It is not easy to be a moderator because of these kind of difficult situations, and I am supporting your answer because of that and because of the answer's main message (above "background"). +1 $\endgroup$ – Andre Silva Aug 29 '13 at 14:49
  • $\begingroup$ I do not agree at all that I used that an ad hominem attack. Some of my comments to you include triple question marks "???" another comment includes stating the same thing for three times (the one about axiom-->theorem-->proof). Probably these annoyed you, and for these I apologize please accept my apology. I will put other comments in a while. $\endgroup$ – Amr Aug 29 '13 at 14:50
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    $\begingroup$ Disclosure: I didn't read the conversation between whuber and @amr before posting my comment of support. Two extra points: We should support whuber's thoroughly reasonable expectation of maintaining a civil tone in discussion. stats.stackexchange.com/questions/2423/… is in fact more nearly a duplicate than the thread previously mentioned. $\endgroup$ – Nick Cox Aug 29 '13 at 14:51
  • $\begingroup$ Regarding complaining about duplicates in meta, I saw it happening before in other SE sites. Thus, I did it here. If it is inappropriate, I did not know it was. Thus, I want to clarify that I did not put this meta post for the purpose of being rude. $\endgroup$ – Amr Aug 29 '13 at 15:08
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    $\begingroup$ Amr I appreciate and accept your apology. The criterion to identify ad hominem comments is clear and simple: any negative assertion, explicit or implied, about another person involved in a discussion is ad hominem. (Sometimes it is legitimate to make polite inquiries about what someone knows or their state of mind, especially when asking for clarification from a poster who appears confused, because you are seeking common ground in order to help them.) As a newcomer to any site if there is any dispute your default assumption should be that perhaps you may be misunderstanding something $\endgroup$ – whuber Aug 29 '13 at 15:10
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    $\begingroup$ There is one more thing that I want to mention and I hope you do not consider it rude: I don't mind my question being closed as a duplicate. However, I mind it when the duplicate does not contain answers for my original question. It is very "frustrating" and "annoying" for me to see my question being closed as a duplicate when the duplicate does not answer my question. This is like making me mute when I need help. Finally, I agree with you that that it is not good to have tensed/stressed conversations and for this reason I apologized. $\endgroup$ – Amr Aug 29 '13 at 15:11
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    $\begingroup$ @whuber OK. I agree with you about the ad hominem point especially when you said: "explicit or implied" $\endgroup$ – Amr Aug 29 '13 at 15:15
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    $\begingroup$ Closure is not permanent. A closed question is in suspense, awaiting a resolution of expressed concerns. As a poster, all you need to do on SE is provide that resolution by means of an edit or a clarifying comment explaining why the question ought to be opened. As moderator I was making an effort to help you provide that resolution by asking for an explanation of how your needs were not met elsewhere here. I anticipated that either you would demonstrate your question should be reopened or else that you would find the answers in the other question. That's how this site is supposed to work! $\endgroup$ – whuber Aug 29 '13 at 15:15
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    $\begingroup$ Two comments to the OP in respect of the answer and comments here): (i) I regularly vote to reopen, as well as to close questions, and I will sometimes make a small edit or comment when I think a post might nearly make it, if I think it will tip it into acceptability without changing the intent. We want to help users with questions where possible (it's not like anyone's getting paid here; you might like to consider what our motives could be); and (ii) if you find yourself suspecting @whuber didn't understand something, bet the other way; that's nearly always how it turns out $\endgroup$ – Glen_b -Reinstate Monica Aug 30 '13 at 0:18
  • $\begingroup$ "it is inappropriate anywhere on StackExchange (and anywhere else civil discourse is valued)" +1 and accept. I am sorry again for what happened yesterday. $\endgroup$ – Amr Aug 30 '13 at 13:18
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I have no problem with your question being reopened.

Meta answer:

I feel in the need to give you some explanation as I have participated in this subject, and this is just my opinion.

I got your question on the first post review queue and I flagged it as a duplicate because even that you have used the word "rigorous", in my first opinion there were two arguments in favor of duplicate (the subject, and the background in statistics) and one against (to be an elementary and rigorous book).
I thought not only there were more arguments in favor to mark the question as duplicate, but I also interpreted the word "rigorous" as being subjective.

I decided to remove the duplicate automatic comment which appears beneath the question, because a experienced user (Nick Cox) argued in favor about the rigorous argument. Then, one of our moderators (other experienced user) ended up marking it as duplicate.

Basically, book recommendation questions are subjective and they carry a side of being opinion-based (far away of being 100% opinion-based, though), and because of that some think they are on-topic (and so far they are!!), some think they should always be set as community wiki posts, and some think they should be off-topic (for the latter two opinions see this thread).

Maybe you can edit your question to specify more about what you are looking for (explaining even better what you mean with rigorous) and giving emphasis about how much different it is from the "duplicate" question. Then, it will go to the "reopen queue" and users will vote if it reopens or stays the way it is.

Remark (not Meta)

Edit: removed this answer part, as the thread was reopened on main site and it received satisfactory answers.

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