## R.R. Bahadur's Lectures on the Theory of Estimation"In the Winter Quarter of the academic year 1984-1985, Raj Bahadur gave a series of lectures on estimation theory at the University of Chicago"--P. i. |

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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

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