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) ...
Read More
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."
Read Less
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good++; Hardcover; Very light wear to the covers with "straight" edge-corners; Small blue ink mark to the top edge, otherwise unblemished textblock edges; The endpapers and text pages are all clean and unmarked; This book will be shipped in a sturdy cardboard box with foam padding; Medium Format (8.5"-9.75" tall); 1.7 lbs; Yellow and white cloth covers with title in black lettering; 1981, Springer-Verlag Publishing; 403 pages; "Statistical Estimation. Asymptotic Theory. Applications of Mathematics, Volume 16, " by I.A. Ibragimov & R.Z. Has'minskii.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good++; Hardcover; Clean covers with minor edgewear; Unblemished textblock edges; The endpapers and all text pages are clean and unmarked; The binding is excellent with a straight spine; This book will be shipped in a sturdy cardboard box with foam padding; Medium Format (8.5"-9.75" tall); 1.7 lbs; Yellow and white cloth covers with title in black lettering; 1981, Springer-Verlag Publishing; 403 pages; "Statistical Estimation. Asymptotic Theory. Applications of Mathematics, Volume 16, " by I.A. Ibragimov & R.Z. Has'minskii.
