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Large adaptive estimation in linear regression model. I: Consistency. (English) Zbl 0792.62033
Summary: A condition of identifiability of linear regression models with symmetric distribution of errors is given. Following R. Beran’s approach [Ann. Stat. 6, 292-313 (1978; Zbl 0378.62051)] for the location case, consistency and asymptotic normality of this adaptive estimator are proved. The result shows that the estimator is not asymptotically efficient. But it selects a model with such distribution function of errors which is (in the sense of Hellinger distance applied to \(F(x)\) and \(1-P(-x))\) “as much as possible symmetric”, which may be useful when we know that there are no reasons for the asymmetry.

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