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I am going through Casella's statistical inference in one-semester standard statistic course and have mathematical background from Sheldon Axler's linear algebra done right and Louis Brand's advanced calculus. I wish to self-study these topics:

  • Lindeberg condition
  • Analysis of variance
  • Akaike Information Criterion
  • Bayesian Information Criterion
  • Eigenvalue decomposition

These are truly divergent topics, so I am wondering are there a single textbook dealing these topics and I can read it from cover to cover? I have much difficulty finding sources covering the last 3 topics, so a source covering the last 3 topics also suffices. My goal is to get full understanding of these topics so a textbook with detailed elaboration will be the best choice.

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As you say, these are very different topics and there is no reason to expect one single book concentrating on those specific topics.

  1. Lindeberg condition is part of (versions of) the central limit theorem, so any probability text covering it. See Book recommendations for probability

  2. Analysis of variance (ANOVA) is a big topic, and book recommendations would depend on what you want it for. Maybe a design of experiment book, or a general linear models book (as ANOVA is a special case.) Or a more practical book like Yandell.

  3. Information criterions can be found in ESL.

  4. Eigenvalue decompositions, again unclear what you want, the linear algebra background or use in statistics? For the last see the previous point.

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For the information criteria I have found very useful Konishi-Kitagawa. Also you may want to look at Burnham-Anderson.

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