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I am taking a course on multivariate statistics and I enjoy it pretty much. But I feel the course focuses too much on procedures and not on answering "why" some things are the way they are.

So let me be more specific. The course is about: - Exploratory and confirmatory factor analysis - Principal Component Analysis - Cluster Analysis - MANOVA - Canonical Correlation Analysis - Discriminant Analysis - Logistic Regression

We are currently following the book "Applied Multivariate Techniques" by Subhash Sharma. I would like to read a book which explains "why" things are the way they are. For example, instead of just saying "We apply the following test", I would like to know what the test statistic means and how we found it. I hope this makes sense.

It can be very mathematically rigorous, I don't mind. It doesn't have to be very proofy (although that would be neat!), but I would like to get to know "why" and not only "how".

user93095
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  • I think each of these methods you listed all has very good motives to solve some particular problems. However, in terms of answering the question "why use this method instead of the other one?", I don't think there is any good justification. I agree with E. T. Jaynes that this is a problem of Frequentist statistics: "Lacking the necessary theoretical principles, they force one to ‘choose a statistic’ from intuition rather than from probability theory, and then to invent ad hoc devices (such as unbiased estimators, confidence intervals, ... – Junpeng Lao Oct 25 '15 at 16:28
  • ... tail-area significance tests) not contained in the rules of probability theory." – Junpeng Lao Oct 25 '15 at 16:28
  • Sorry to break up the comment like this - I dont really have a good answer to your question, but from a different angle maybe you can have a look of E. T. Jaynes's Probability Theory or Jeffery's Probability Theory – Junpeng Lao Oct 25 '15 at 16:29
  • Other possible dup targets: https://stats.stackexchange.com/questions/2181/book-recommendations-for-multivariate-analysis https://stats.stackexchange.com/questions/414/introduction-to-statistics-for-mathematicians – kjetil b halvorsen Sep 02 '18 at 12:52

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