Geodesic
Estimating a~monotone function, being observe in the white noise
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 124-133

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Monotone functions on the segment is being observed in the Gaussian white noise. The Maximum Likelihood Estimator of such a function is of a piecewise continious sort. A limit theorem on the convergence rate of such an estimator is proved. 
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     author = {K. L. Zilberburg},
     title = {Estimating a~monotone function, being observe in the white noise},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {124--133},
     publisher = {mathdoc},
     volume = {341},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a6/}
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K. L. Zilberburg. Estimating a~monotone function, being observe in the white noise. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 124-133. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a6/