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On adaptive estimation of linear functionals
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DOI：10.1214/009053605000000633.png)
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摘要
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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.
Keyword:
adaptive estimation
between-class modulus of continuity
cost of adaptation
linear functional
ordered modulus of continuity
white noise model
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3.7
论文数:
2.8K
被引数:
2.9W
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