Estimating a smooth monotone regression function
The problem of estimating a smooth monotone regression function mmm will be studied. We will consider the estimator mSImSIm_{SI} consisting of a smoothing step (application of a kernel estimator based on a kernel KKK) and of a isotonisation step (application of the pool adjacent violator algorithm)....
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1991
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| In: |
The annals of statistics
Year: 1991, Volume: 19, Issue: 2, Pages: 724-740 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176348117 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/aos/1176348117 Verlag, Volltext: https://projecteuclid.org/euclid.aos/1176348117 Verlag, Volltext: https://projecteuclid.org/download/pdf_1/euclid.aos/1176348117 
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| Author Notes: | Enno Mammen |
| Summary: | The problem of estimating a smooth monotone regression function mmm will be studied. We will consider the estimator mSImSIm_{SI} consisting of a smoothing step (application of a kernel estimator based on a kernel KKK) and of a isotonisation step (application of the pool adjacent violator algorithm). The estimator mSImSIm_{SI} will be compared with the estimator mISmISm_{IS} where these two steps are interchanged. A higher order stochastic expansion of these estimators will be given which show that mSImSIm_{SI} and mSImSIm_{SI} are asymptotically first order equivalent and that mISmISm_{IS} has a smaller mean squared error than mSImSIm_{SI} if and only if the kernel function of the kernel estimator is not too smooth. |
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| Item Description: | First available in Project Euclid: 12 April 2007 Gesehen am 27.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/aos/1176348117 |