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Theory & Methods: On Estimators of Scale and Dispersion in Neighbourhoods ofParametric Families
Author(s) -
Lee S.J.
Publication year - 2000
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00137
Subject(s) - mathematics , estimator , parametric statistics , statistics , upper and lower bounds , scale (ratio) , dispersion (optics) , degree (music) , distribution (mathematics) , efficiency , asymmetry , econometrics , mathematical analysis , geography , physics , cartography , quantum mechanics , acoustics , optics
This paper investigates two estimators under the non‐parametric neighbourhoods of an exponential scale parametric family. It uses the relative efficiency approach and shows that the tighter lower bounds on the relative efficiency of the upper trimmed mean to mean can be obtained under a sufficient condition. This condition gives the relationship between the possible positive lower bound and the degree of asymmetry of some related distributions. Similar arguments can be applied to the comparison of dispersion estimators under the neighbourhoods of a normal distribution.