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I'm very familiar with a lot of undergraduate to M.S.-level textbooks, as well as measure-theoretic textbooks, but I'm not at all knowledgeable about Ph.D. methods texts.

Namely, there's a Ph.D. methods course which has the following description:

Methods of constructing complex models including adding parameters to existing structures, incorporating stochastic processes and latent variables. Use of modified likelihood functions; quasi-likelihoods; profiles; composite likelihoods. Asymptotic normality as a basis of inference; Godambe information. Sample reuse; block bootstrap; resampling with dependence. Simulation for model assessment. Issues in Bayesian analysis.

I would really like to start learning this information. What is/are suitable textbook(s) which cover the material above?

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According to your descriptions, here are some good ones:

  • Theory of Statistics by Mark Schervish (an ideal book to prepare qualifying exams)
  • Mathematical Statistics by Jun Shao (somewhat hard to read, very math intensive)
  • Mathematical Statistics: Basic Ideas and Selected Topics by Peter Bickel, et al.
  • Theoretical Statistics by Robert Keener
  • Bayesian Data Analysis by Andrew Gelman, et al. (more applied)

Hope it helps.

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