Abstract
AbstractThe least‐absolute‐deviation estimate of a monotone regression function on an interval has been studied in the literature. If the observation points become dense in the interval, the almost sure rate of convergence has been shown to be O(n1/4). Applying the techniques used by Brunk (1970, Nonparametric, Techniques in Statistical Inference. Cambridge Univ. Press), the asymptotic distribution of the l1 estimator at a point is obtained. If the underlying regression function has positive slope at the point, the rate of convergence is seen to be O(n1/3). Monotone percentile regression estimates are also considered.
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