A comparative study of monotone nonparametric kernel estimates

In this paper we present a detailed numerical comparison of three monotone nonparametric kernel regression estimates, which isotonize a nonparametric curve estimator. The first estimate is the classical smoothed isotone estimate of Brunk (1958). The second method has recently been proposed by Hall and Huang (2001) and modifies the weights of a commonly used kernel estimate such that the resulting estimate is monotone. The third estimate was recently proposed by Dette, Neumeyer and Pilz (2003) and combines density and regression estimation techniques to obtain a monotone curve estimate of the inverse of the isotone regression function. The three concepts are briefly reviewed and their finite sample properties are studied by means of a simulation study. Although all estimates are first order asymptotically equivalent (provided that the unknown regression function is isotone) some differences for moderate samples are observed.