Statistical Performance of Location Estimators |
Contents
INTRODUCTION 115 | 1 |
THE BEHAVIOR OF LOCATION ESTIMATORS UNDER A FIXED DENSITY | 15 |
THE BEHAVIOR OF LOCATION ESTIMATORS OVER A CLASS OF DENSITIES 55 5 5 5 5 | 55 |
4 other sections not shown
Common terms and phrases
²au absolutely continuous density adaptive estimators Cauchy-Schwarz inequality consequence convergence COROLLARY Cramér-Rao bound Cramér-Rao inequality defined denote densities f(•-0 density f derivative f dichtheid differentiable dominated convergence theorem E₂ equal zero estimator of location F t)dt Fatou's lemma finite Fisher information fixed sample Fubini's theorem Furthermore Hence holds implies integrated mean square K¹(u Laat Lebesgue measure Let f Let H liminf limsup location estimators loss functions lower bound mators mean square error measurable function nI(f obtain Pitman estimator proefschrift prove random variables result satisfies schatter score function Section sin[en standard normal distribution standard normal random statistical situation subsets symmetric about zero symmetric distribution function T₂ translation equivariant estimators truncated variance verdeling X₁ yields zijn ε ε