Monotone estimation for the coefficient functions of varying coefficient models

As a useful semiparametric learning method, varying coefficient models mitigate the "curse of dimensionality" of full nonparametric models while retain interpretability and flexibility in modelling. In certain applications, monotone coefficient functions are needed in the varying coefficient models. In this paper, we propose a monotone estimation procedure for the coefficient functions in the varying coefficient models. The proposed method not only ensures monotone estimates, but also reduces mean squared errors in estimation for such coefficient functions. Furthermore, this method is computationally efficient as it does not require constrained optimization. The asymptotic normality of the monotone coefficient function estimator is established, and numerical studies are conducted to demonstrate the practicality and advantages of the proposed method.