Conditionally parametric models of the covariate-response type are considered. The estimation of the unknown link function can be done using non-parametric methods. The shape-restriction and smoothness assumptions are taken into account for scientific purposes. Applications include isotonic regression, current status models, hazard- vulnerability rates etc. We discuss the likelihood-ratio method briefly and the smoothing spline method. Using a penalized least square method to incorporate both smoothness and monotonicity, we develop a scheme to produce functional estimates of the unknown link function. Point-wise confidence sets can be produced for the regression curve.