| 书目名称 | Statistical Estimation | | 副标题 | Asymptotic Theory | | 编辑 | I. A. Ibragimov,R. Z. Has’minskii | | 视频video | | | 丛书名称 | Stochastic Modelling and Applied Probability | | 图书封面 |  | | 描述 | 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 asymptotically 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 evalua | | 出版日期 | Book 1981 | | 关键词 | Asymptotische Wirksamkeit; Estimation Theory; Estimator; Parameter; Schätzung (Statistik) | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4899-0027-2 | | isbn_ebook | 978-1-4899-0027-2Series ISSN 0172-4568 Series E-ISSN 2197-439X | | issn_series | 0172-4568 | | copyright | Springer Science+Business Media New York 1981 |
The information of publication is updating
|
|
发表于 2025-3-21 20:08:16
