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Expected Absolute Error of the Usual Estimator of the Binomial Parameter

 

作者: ColinR. Blyth,  

 

期刊: The American Statistician  （Taylor Available online 1980）
卷期: Volume 34, issue 3  

页码: 155-157

 

ISSN:0003-1305

 

年代: 1980

 

DOI:10.1080/00031305.1980.10483022

 

出版商: Taylor & Francis Group

 

关键词: Binomial and Poisson distributions;Point estimation;Standard error;Average error;Mean deviation;Expected absolute error

 

数据来源: Taylor

 

摘要:

ForXwith binomial (n, p) distribution the usual measure of the error ofX/nas an estimator ofpis its standard errorSn(p)= √{E(X/n – p)2} = √{p(1 –p)/n}. A somewhat more natural measure is the average absolute errorDn(p) = E‖X/n – p‖. This article considers use ofDn(p)instead ofSn(p)in a student's first introduction to statistical estimation. Exact and asymptotic values ofDn(p), and the appearance of its graph, are described in detail. The same is done for the Poisson distribution.

 

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