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Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of.

**Table of contents**

- Wiley Series in Probability and Statistics | Awards | LibraryThing
- Approximation Theorems of Mathematical Statistics (Wiley Series in Probability and Statistics)
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## Wiley Series in Probability and Statistics | Awards | LibraryThing

I am not sure what comprises the current set, but any or all of the books are useful. Lehmann, E. Romano , Testing Statistical Hypotheses, third edition, Springer. There is a useful companion book called Testing Statistical Hypotheses: Worked Solutions by some people at CWI in Amsterdam that has solutions to the exercises in the first edition. Most of these are also in the third edition.

Stuart, A. Schervish, Mark J. This rigorous and quite comprehensive text has a Bayesian orientation. Shao, Jun , Mathematical Statistics, second edition, Springer.

## Approximation Theorems of Mathematical Statistics (Wiley Series in Probability and Statistics)

Comprehensive and rigorous; better than the first edition. Solutions or partial solutions to some exercises in Shao , plus some additional exercises and solutions. Texts in probability and measure theory and linear spaces roughly at the level of this course B. Fristedt and L. Accessible and wide-ranging text; also covers stochastic calculus.

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Athreya, Krishna B. A very solid book, but beware of typos in the first printing. This is one of the best books on probability and measure theory for probability, in terms of coverage and rigor. No explicit coverage of linear spaces. Breiman, Leo , Probability, Addison-Wesley.

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This is a classic book on measure-theoretic-based probability theory. No explicit coverage of measure theory or linear spaces.

Dudley, R. Accessible and comprehensive.

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Texts that provide good background for this course Berger, James O. Bickel, Peter, and Kjell A. This book covers material from Chapters and Chapter 10 of the first edition, but with more emphasis on nonparametric and semiparametric models and on function-valued parameters. It also includes more Bayesian perspectives. The second volume will not appear for a couple of years.

In the meantime, the first edition remains a very useful text.

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Stein operators for product distributions, with applications. Distributional transformations, orthogonal polynomials, and Stein characterizations, Journal of Theoretical Probability 18 , — Rate of convergence to the semi-circular law, Probability Theory and Related Fields , — Limit theorems for spectra of random matrices with martingale structure, Teor.

The rate of convergence in law of the maximum of an exponential sample, Statistica Neerlandica 33 , — Fisher information inequalities and the central limit theorem, Probability Theory and Related Fields , — On an inequality of Chernoff, Annals of Probability 13 , — On characterizations of distributions by mean absolute deviation and variance bounds, Annals of the Institute of Statistical Mathematics 43 , — Extension of the fourth moment theorem to invariant measures of diffusions, preprint arXiv Generalized Pearson distributions and related characterization problems, Annals of the Institute of Statistical Mathematics 54 , — Distances between nested densities and a measure of the impact of the prior in Bayesian statistics, Annals of Applied Probability , to appear.

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Parametric Stein operators and variance bounds, Brazilian Journal of Probability and Statistics 30 , — Multivariate Stein factors for a class of strongly log-concave distributions. Electronic Communications in Probability 21 paper no.

Entropy and the fourth moment phenomenon, Journal of Functional Analysis , — On a system of discrete distributions, Biometrika 54 , — A characterization of the Pearson system of distributions and the associated orthogonal polynomials, Annals of the Institute of Statistical Mathematics 47 , — Degree asymptotics with rates for preferential attachment random graphs, Annals of Applied Probability 23 , — Probability Metrics and the Stability of Stochastic Models , vol.

Discrete Math.

A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability Univ. California, Berkeley, Calif. II: Probability theory Berkeley, Calif. California Press , —