Statistical Estimation. Asymptotic Theory. Applications of Mathematics, Volume 16

Ibragimov, I.A.,Has'minskii, R.Z.

ISBN 10: 0387905235 / ISBN 13: 9780387905235

Verlag: Springer, 1981

Beschreibung

previous owner's name in front, English edition, number 16 Good hardcover with some shelfwear; may have previous owner's name inside. Standard-sized.

Bestandsnummer des Verkäufers mon0000295314

Bibliografische Details

• Titel: Statistical Estimation. Asymptotic Theory. Applications of Mathematics, Volume 16
• Verlag: Springer
• Erscheinungsjahr: 1981
• Sprache: Englisch
• ISBN-10: 0387905235
• ISBN-13: 9780387905235
• Einband: hardcover
• Zustand: Good

Über diesen Titel

Inhaltsangabe

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 evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.