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Wednesday, November 1, 2000 - 3:00pm

T. Tony Cai

The Wharton School

Location

The Wharton School

SH-DH 351

Refreshments will be served.

Orthogonal series methods have been well developed in nonparametric function estimation. Among them, separable rules have drawn particular attention. For example, in deriving the minimax risk for estimating functions over Besov classes using a wavelet basis, Donoho and Johnstone (1998, Ann. Statist. pp. 879-921) showed that the least favorable priors necessarily have independent coordinates and the Bayes minimax rules are separable. In this talk we explore the connection between information pooling and adaptability. We demonstrate that information pooling is a key to increase estimation precision and achieve adaptability and even superefficiency. We first show that separable rules lack adaptability; they are necessarily not rate-adaptive. A sharp lower bound on the cost of adaptation for separable rules is derived. We then derive a tight lower bound on the amount of information pooling required for achieving global adaptability. Moreover, in a sharp contrast to the separable rules, it is shown that adaptive nonseparable rules can be superefficient at every point in the parameter spaces. Some numerical results will also be discussed.