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M‐estimation in the presence of unequal scale
Author(s) -
Cressie Noel
Publication year - 1980
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1980.tb00682.x
Subject(s) - estimator , mathematics , inefficiency , variance (accounting) , statistics , scale (ratio) , minimum variance unbiased estimator , estimation , class (philosophy) , delta method , econometrics , computer science , economics , accounting , management , artificial intelligence , microeconomics , physics , quantum mechanics
The class of weighted M‐estimators is defined. The ratio of the asymptotic variance of the weighted estimator to the asymptotic variance of the optimally weighted estimator is defined as the inefficiency. A K antorovich inequality is proved, its implications are investigated for the misweighted mean and misweighted median, and the results are applied to a batch of demographic data.