Convergence rate of b-spline estimators of nonparametric conditional quantile functions∗
- 1 January 1994
- journal article
- research article
- Published by Taylor & Francis Ltd in Journal of Nonparametric Statistics
- Vol. 3 (3-4), 299-308
- https://doi.org/10.1080/10485259408832589
Abstract
Given a bivariate sample {(Xi,Yi), i = 1,2,…, n}, we consider the problem of estimating the conditional quantile functions of nonparametric regression by minimizing ∑ρα(Yi-g(Xi)) over g in a linear space of B-spline functions, where ρα(u) = |u| - (2α - 1)u is the Czech function of Koenker and Bassett (1978). If the true conditional quantile function is smooth up to order r, we show that the optimal global convergence rate of n -r/(2r+1) is attained by the B-spline based estimators if the number of knots is in the order of n 1/(2r+1).Keywords
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