## ＜電子ブック＞Statistical Estimation : Asymptotic Theory

責任表示 by I. A. Ibragimov, R. Z. Has'minskii Ibragimov, I. A Has'minskii, R. Z SpringerLink (Online service) English (英語) Springer New York Imprint: Springer 1981- New York, NY, United States シリーズ Applications of Mathematics, Applied Probability Control Economics Information and Communication Modeling and Identification Numerical Techniques Optimization ; 16 when certain parameters in the problem tend to limiting values (for example, when the sample size increases indefinitely, the intensity of the noise ap proaches zero, etc.) To address the problem of a...symptotically optimal estimators consider the following important case. Let X 1, X 2, ... , X n be independent observations with the joint probability density !(x,O) (with respect to the Lebesgue measure on the real line) which depends on the unknown patameter o e 9 c R1. It is required to derive the best (asymptotically) estimator 0:( X b ... , X n) of the parameter O. The first question which arises in connection with this problem is how to compare different estimators or, equivalently, how to assess their quality, in terms of the mean square deviation from the parameter or perhaps in some other way. The presently accepted approach to this problem, resulting from A. Wald's contributions, is as follows: introduce a nonnegative function w(0l> ( ), Ob Oe 9 (the loss function) and given two estimators Of and O! n 2 2 the estimator for which the expected loss (risk) Eown(Oj, 0), j = 1 or 2, is smallest is called the better with respect to Wn at point 0 (here EoO is the expectation evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.続きを見る Basic NotationThe Problem of Statistical EstimationLocal Asymptotic Normality of Families of DistributionsProperties of Estimators in the Regular CaseSome Applications to Nonparametric EstimationIndependent Identically Distributed Observations. Densities with JumpsIndependent Identically Distributed Observations. Classification of SingularitiesSeveral Estimation Problems in a Gaussian White Noise. Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

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レコードID 3644041 QA273.A1-274.9 QA274-274.9 519.2 Mathematics. Distribution (Probability theory). Mathematics. Probability Theory and Stochastic Processes. ssj0001091965 9781489900296(print) 9781489900272 2020.06.27 2020.06.28