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On information pooling, adaptability and superefficiency in nonparametric function estimation

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  • Cai, T. Tony

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.

Suggested Citation

  • Cai, T. Tony, 2008. "On information pooling, adaptability and superefficiency in nonparametric function estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 421-436, March.
  • Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:421-436
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    Cited by:

    1. Florent Autin & Jean-Marc Freyermuth & Rainer Von Sachs, 2014. "Block-threshold-adapted Estimators via a Maxiset Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 240-258, March.

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