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

0 avg rating
( 0 ratings by Goodreads )
 
9780387905235: Statistical Estimation. Asymptotic Theory. Applications of Mathematics, Volume 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 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.

"synopsis" may belong to another edition of this title.

Buy New View Book
List Price: US$ 99.00
US$ 603.99

Convert Currency

Shipping: US$ 1.99
Within U.S.A.

Destination, Rates & Speeds

Add to Basket

Top Search Results from the AbeBooks Marketplace

1.

Ibragimov, I.A., Has'minskii, R.Z.
Published by Springer (1981)
ISBN 10: 0387905235 ISBN 13: 9780387905235
New Hardcover Quantity Available: 1
Seller:
Murray Media
(North Miami Beach, FL, U.S.A.)
Rating
[?]

Book Description Springer, 1981. Hardcover. Book Condition: New. Never used!. Bookseller Inventory # P110387905235

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 603.99
Convert Currency

Add to Basket

Shipping: US$ 1.99
Within U.S.A.
Destination, Rates & Speeds