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Asymptotic equivalence for nonparametric regression with multivariate and random design. (English) Zbl 1142.62023
Summary: We show that nonparametric regression is asymptotically equivalent, in Le Cam’s sense [L. Le Cam and G. Lo Yang, Asymptotics in statistics. Some basic concepts. 2nd ed. (2000; Zbl 0952.62002)], to a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework, based on approximation spaces, which allows asymptotic equivalence to be achieved, even in the cases of multivariate and random designs.

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62B15 Theory of statistical experiments
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