Commonly used kernel regression estimators may not provide admissible values of the regression function or its functionals at the boundaries, for regressions with restricted support. Any smoothing method will become less accurate near the boundary of the observation interval because fewer observations can be averaged, and thus variance or bias can be affected. Here, we adapt Chaubey et al. (2007)'s method of density estimation for nonnegative random variables to define a smooth estimator of the regression function. The estimator is based on a generalization of Hille's lemma and a perturbation idea. Its uniform consistency and asymptotic normality are obtained, for the sake of generality, under a stationary ergodic process assumption for the data . The asymptotic mean squared error is derived and the optimal value of
smoothing parameter is also discussed. Graphical illustration of the proposed estimator are provided on
simulated as well as real-life data.