Abstract
The asymptotic behavior of the isotonic estimator of a monotone regression function (that is the least-squares estimator under monotonicity restriction) is investigated. In particular it is proved that the ?1-distance between the isotonic estimator and the true function is of magnitude n-1/3. Moreover, it is proved that a centered version of this ?1-distance converges at the n1/2 rate to a Gaussian variable with fixed variance.
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