On Information Pooling, Adaptability And Superefficiency in Nonparametric Function Estimation
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