On nonparametric regression estimators based on regression quantiles
- 1 January 1987
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 16 (2) , 383-396
- https://doi.org/10.1080/03610928708829374
Abstract
In the ciassical regression model Yi=h(xi) + ∊ i, i=1,…,n, Cheng (1984) introduced linear combinations of regression quantiles as a new class of estimators for the unknown regression function h(x). The asymptotic properties studied in Cheng (1984) are reconsidered. We obtain a sharper scrong consistency rate and we improve on the conditions for asymptotic normality by proving a new result on the remainder term in the Bahadur representation for regression quantiles.Keywords
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- The central limit theorem for dependent random variablesDuke Mathematical Journal, 1948