Robust nonparametric estimation of monotone regression functions with interval-censored observations

Nonparametric estimation of monotone regression functions is a classical problem of practical importance. Robust estimation of monotone regression functions in situations involving interval-censored data is a challenging yet unresolved problem. Herein, we propose a nonparametric estimation method based on the principle of isotonic regression. Using empirical process theory, we show that the proposed estimator is asymptotically consistent under a specific metric. We further conduct a simulation study to evaluate the performance of the estimator in finite sample situations. As an illustration, we use the proposed method to estimate the mean body weight functions in a group of adolescents after they reach pubertal growth spurt.