## R.R. Bahadur's Lectures on the Theory of EstimationThis e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press. |

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a.e. with respect affine function Approach arbitrary assume asymptotic attained Bayes estimate Bhattacharya bound Borel functions C-R bound Cauchy Cauchy-Schwarz INEQUALItY Chicago Conditions 1-3 continuous counting measure Cramer-Rao density depends on 9 differentiable distribution dPg(s Ee(t Eg(t equality iff Es(t estimate of 9 estimating 9 estimation theory Example 1(a exists Fisher information Fisher's bound follows G Ug G Wg given 9 hence Homework inequality Lebesgue measure Lecture linear LMVU LMVUE minimax ML estimate neighborhood Neyman-Pearson lemma Note one-parameter exponential family orthogonal projection parameter Pe(A positive definite Proof Qs,e Raj Bahadur Raj's respect to Lebesgue risk function sample score function sequence space Span{l Statistical Inference subspace subspace spanned sufficient statistic sufficiently small Suppose t e Ug theorem Ug is non-empty UMVUE unbiased estimate Vare(t Varfl(t variance vector Wg contains

### Popular passages

Page 75 - On Fisher's Bound for Stable Estimators with Extension to the Case of Hubert Parameter Space.