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The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic Asymptotic Methods in Statistical Decision Theory. This book grew out of lectures delivered at the University of California, Berkeley, over many years. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts.
The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer  or the more recent text by P. Another pos sibility, closer to the present in spirit, is Ferguson . Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions.
Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation.
Approximation Properties for Likelihood Ratios. Equivalent Definitions for Sufficiency. Limit Theorems and Related Results. Sums of Independent Stochastic Processes. Limiting Distributions for Likelihood Ratios. Conditions for Asymptotic Normality.
Estimates for Finite Dimensional Parameter Spaces. The Risk of Formal Bayes Procedures. A Result on Asymptotic Admissibility. A Lifting Theorem and Some Applications. An Application of a Martingale Limit Theorem. Definitions Relative to Quadratic Approximations. The Asymptotically Gaussian Case.
Reduction to the Gaussian Case by Small Distortions. Minimum X and Relatives. Remarks on Possible Applications. A Lemma on Approximate Sufficiency. Homogeneous Experiments of Finite Rank. Approximation by Experiments of Finite Rank. Construction of Distinguished Sequences of Estimates.
Poisson Exponentials and Approximation Theorems. Empirical Measures and Cumulatives. Empirical Measures on VapnikCervonenkis Classes. Hilbert Spaces Around a Point.
Differentiability in Quadratic Mean. Asymptotic Normality for Rates Other than Vn. Existence of Consistent Estimates. Estimates Converging at the VnRate. The Behavior of Posterior Distributions. Results from Classical Analysis. Vector Lattices Arising from Experiments. Lattices of Numerical Functions. Extensions of Positive Linear Functions.