I am currently a second-year graduate student in statistics. I have taken the course with the textbook Statistical inference by George Casella and Roger L. Berger.

I have learned some basic concepts such as sufficient statistics, complete sufficient statistics, UMVUE and etc. Though I found all these concepts are in one-dimensional case in this book. Can anyone recommend a book that covers these concepts in a multivariate or high dimensional case? Especially, a textbook with practice questions and a solution manual is preferred.

  • $\begingroup$ Could you elaborate on what exactly you mean by 'one-dimensional case' regarding the topics you mentioned? I guess multivariate extensions of these topics are often immediate, so they are not specifically discussed. $\endgroup$ Mar 29, 2020 at 20:36
  • $\begingroup$ It is not multivariate problems. For example, the majority of the problems do not use matrix and vectors. $\endgroup$
    – Olivia
    Apr 2, 2020 at 2:13
  • $\begingroup$ You can check out Theory of Point Estimation by E.L. Lehmann (there are two other books by the same author on hypothesis testing and asymptotic theory) and Mathematical Statistics by Shao. Both of these are advanced texts on inference. $\endgroup$ Apr 22, 2020 at 20:14


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