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On information pooling, adaptability and superefficiency in nonparametric function estimation

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  • Cai, T. Tony
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    Abstract

    The connections between information pooling and adaptability as well as superefficiency are considered. Separable rules, which figure prominently in wavelet and other orthogonal series methods, are shown to lack adaptability; they are necessarily not rate-adaptive. A sharp lower bound on the cost of adaptation for separable rules is obtained. We show that adaptability is achieved through information pooling. A tight lower bound on the amount of information pooling required for achieving rate-optimal adaptation is given. Furthermore, in a sharp contrast to the separable rules, it is shown that adaptive non-separable estimators can be superefficient at every point in the parameter spaces. The results demonstrate that information pooling is the key to increasing estimation precision as well as achieving adaptability and even superefficiency.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 99 (2008)
    Issue (Month): 3 (March)
    Pages: 421-436

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    Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:421-436

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    Related research

    Keywords: Adaptability Bayes rules Information pooling Minimax Minimum risk inequalities Nonparametric regression Orthogonal series Separable rules Superefficiency Wavelets White noise;

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