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Non-parametric applications of an infinite dimensional convolution theorem. (English) Zbl 0571.62031

It is shown that the Hajék-Le Cam convolution theorem also holds for shift experiments in abstract Wiener spaces. The result is applied to efficient estimation of various nonparametric quantities. In most cases this is achieved by evaluating statistical functionals at the empirical distribution.
Reviewer: W.Stute

MSC:

62G05 Nonparametric estimation
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
62G20 Asymptotic properties of nonparametric inference
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