Adaptive estimation in linear regression model. II: Asymptotic normality. (English) Zbl 0792.62034

Summary: [For part I see the preceding review, Zbl 0792.62033.]
An asymptotic representation of an adaptive estimator based on R. Beran’s idea [Ann. Stat. 6, 292-313 (1978; Zbl 0378.62051)] of minimizing Hellinger distance is derived. It is shown that the estimator is asymptotically normal but not efficient. From the practical point of view the approach may be useful because it selects a model with distribution of residuals symmetric “as much as possible” (in the sense of Hellinger distance applied to \(F(x)\) and \(1-F(x)\)). It is not difficult to construct a numerical example showing that sometimes it is the only way how to find a proper model.


62G07 Density estimation
62G35 Nonparametric robustness
62G20 Asymptotic properties of nonparametric inference
62F35 Robustness and adaptive procedures (parametric inference)
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