On Adaptive Estimation of Linear Functionals
Tony Cai and Mark Low
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Abstract:
Adaptive estimation of linear functionals over a collection of
parameter spaces is considered. A between class modulus
of continuity, a geometric quantity, is shown to be instrumental in
characterizing the degree of adaptability over two parameter spaces in
the same way that the usual modulus of continuity captures the minimax
difficulty of estimation over a single parameter space. A general
construction of optimally adaptive estimators based on an ordered
modulus of continuity is given. The results are complemented by
several illustrative examples.
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