MARC Record from harvard_bibliographic_metadata

LEADER: 03453nam a22004575a 4500
001 014158159-X
005 20141003190504.0
008 130815s1981 xxu| o ||0| 0|eng d
020 $a9781489900272
020 $a9781489900296 (ebk.)
020 $a9781489900272
020 $a9781489900296
024 7 $a10.1007/978-1-4899-0027-2$2doi
035 $a(Springer)9781489900272
040 $aSpringer
050 4 $aQA273.A1-274.9
050 4 $aQA274-274.9
072 7 $aMAT029000$2bisacsh
072 7 $aPBT$2bicssc
072 7 $aPBWL$2bicssc
082 04 $a519.2$223
100 1 $aIbragimov, I. A.,$eauthor.
245 10 $aStatistical Estimation :$bAsymptotic Theory /$cby I. A. Ibragimov, R. Z. Has’minskii.
264 1 $aNew York, NY :$bSpringer New York :$bSpringer,$c1981.
300 $aVII, 403 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aApplications of Mathematics, Applied Probability Control Economics Information and Communication Modeling and Identification Numerical Techniques Optimization,$x0172-4568 ;$v16
505 0 $aBasic Notation -- The Problem of Statistical Estimation -- Local Asymptotic Normality of Families of Distributions -- Properties of Estimators in the Regular Case -- Some Applications to Nonparametric Estimation -- Independent Identically Distributed Observations. Densities with Jumps -- Independent Identically Distributed Observations. Classification of Singularities -- Several Estimation Problems in a Gaussian White Noise.
520 $awhen 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 evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.
650 10 $aMathematics.
650 0 $aDistribution (Probability theory)
650 0 $aMathematics.
650 24 $aProbability Theory and Stochastic Processes.
700 1 $aHas’minskii, R. Z.,$eauthor.
776 08 $iPrinted edition:$z9781489900296
830 0 $aApplications of Mathematics, Applied Probability Control Economics Information and Communication Modeling and Identification Numerical Techniques Optimization ;$v16.
988 $a20140910
906 $0VEN