Monotone Function Estimation in Varying Coefficient Model

Abstract

Function estimation under shape constraints is gaining great popularity among statisticians and particularly, monotone function estimation has been studied extensively. This paper introduces function estimation methods in the varying coefficient model when the coefficient functions are monotone. To estimate the coefficient functions, we have to consider the covariate effect, which enter into the weights in the varying coefficient model. We first review the estimation method and algorithm in the traditional regression model and see how this method can be extended to the additive model. Then, we present formulation and algorithm of monotone function estimation in the varying coefficient model by adapting the minimization problem to the traditional case. We also attempt to extend this model to more generalized varying coefficient model where only some part of the coefficient functions enters into the model. Finally, we carry out numerical studies with simulated data.