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Statistical Estimation: Asymptotic Theory (Stochastic Modelling and Applied Probability) free ebook download

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Author(s):	I.A. Ibragimov

Date:	June 30, 1981	Format:	djvu	Language:	English	ISBN/ASIN:	0387905235
Pages:	1	OCR:		Quality:		ISBN13:	9780387905235
Uploader:	tvladb77	Upload Date:	9/1/2022 12:12:48 PM

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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.

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Tags: Applied Asymptotic Estimation Modelling Probability Statistical Stochastic Theory

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Statistical Estimation: Asymptotic Theory (Stochastic Modelling and Applied Probability) free ebook download

Category: Statistics

Description: Click to see full description

Category:
Statistics