Bernstein Polynomial Estimation in the Partially Linear Model under Monotonicity Constraints

In this paper, a Bernstein-polynomial-based likelihoodmethod is proposed for the partially linear model under monotonicity constraints.Monotone Bernstein polynomials are employed to approximate the monotonenonparametric function in the model. The estimator of the regression parameteris shown to be asymptotically normal and efficient, and the rate of convergenceof the estimator of the nonparametric component is established, which could bethe optimal under the smooth assumptions. A simulation study and a real dataanalysis are conducted to evaluate the finite sample performance of the proposedmethod.