Maximum likelihood estimation of mixture constants and locally optimal detection of contaminants

✍ Scribed by Douglas J. Warren; John B. Thomas

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 623 KB
• Volume: 326
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(89)90050-1

✦ Synopsis

The problems of asymptotic M-estimation of mixture constants and local detection of the presence of contaminating distributions are considered. The asymptotic variance of consistent M-estimators is found and it is shown that this variance is minimized by the maximum likelihood estimate (ML@. Conditions are found for the consistency and asymptotic normality of M-estimators and it is shown that the A4LE satisfies these conditions,

The eficacy for a test designed to detect the presence of vanishingly small contaminants is &fined. The detector which maximizes the eficacy is found and it is shown that the detector nonlinearity which maximizes the eficacy is the same as the MLE nonlinearity. Furthermore, it is shown that, as in the case of the MLEfor location and the optimal small signal detector, the eficacy of the locally optimal detector and the asymptotic variance of the iULE are inversely related.