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Asymptotic equivalence of nonparametric autoregression and nonparametric regression. (English) Zbl 1246.62105

Summary: We prove that nonparametric autoregression is asymptotically equivalent in the sense of Le Cam’s deficiency distance to nonparametric regression with random designs as well as with regular nonrandom designs.

MSC:

62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G20 Asymptotic properties of nonparametric inference
62B15 Theory of statistical experiments

References:

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