Premium
LOWER BOUNDS FOR THE DIVERGENCE OF DIRECTIONAL AND AXIAL ESTIMATORS
Author(s) -
Kakarala Ramakrishna,
Watson Geoffrey S.
Publication year - 1997
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1997.tb00690.x
Subject(s) - estimator , divergence (linguistics) , mathematics , projector , upper and lower bounds , unit vector , unit sphere , combinatorics , von mises yield criterion , mathematical analysis , statistics , computer science , physics , finite element method , philosophy , linguistics , thermodynamics , computer vision
Summary Consider estimation of a unit vector parameter a in two classes of distributions. In the first, α is a direction. In the second, α is an axis, so that –α and α are equivalent: the aim is to obtain the projector αα t . In each case the paper uses first principles to define measures of the divergence of such estimators and derives lower bounds for them. These bounds are computed explicitly for the Fisher‐Von Mises and Scheidegger‐Watson densities on the g‐dimensional sphere, ω q . In the latter case, the tightness of the bound is established by simulations.