Estimating a smooth monotone regression function - Mammen, Enno (The annals of statistics, 1991)
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.