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 n 1/2 rate to a Gaussian variable with fixed variance.
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Received: 20 September 1999 / Revised version: 10 May 2001 / Published online: 19 December 2001
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Durot, C. Sharp asymptotics for isotonic regression. Probab Theory Relat Fields 122, 222–240 (2002). https://doi.org/10.1007/s004400100171
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DOI: https://doi.org/10.1007/s004400100171
Keywords
- Asymptotic Behavior
- Regression Function
- True Function
- Fixed Variance
- Gaussian Variable