On Adaptive Estimation of Linear Functionals1 by T. Tony Cai
نویسنده
چکیده
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.
منابع مشابه
Adaptive Functional Linear Regression
Theoretical results in the functional linear regression literature have so far focused on minimax estimation where smoothness parameters are assumed to be known and the estimators typically depend on these smoothness parameters. In this paper we consider adaptive estimation in functional linear regression. The goal is to construct a single data-driven procedure that achieves optimality results ...
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