Stat 8112 Lecture Notes The Wald Consistency Theorem
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چکیده
A topological space is a Borel space if it is homeomorphic to a Borel subset of a Polish space (Bertsekas and Shreve, 1978, Definition 7.7). Examples of Borel spaces include any Borel subset of a Euclidean space Rd and, more generally, any Borel subset of a Polish space (Bertsekas and Shreve, 1978, Proposition 7.12). If X and Y are Borel spaces, a function g : X × Y → R is upper semianalytic if for every c ∈ R the set
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STAT 566 Fall 2013 Statistical Inference Lecture Notes
2 Lecture 2: Evaluation of Statistical Procedures I 2 2.1 How to compare δ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Comparing risk function I: Bayes risk . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Bayes theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Bayes risk revisited . . . . . . . . . . . . . . . . . . . . . . . . . ...
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