Monotone B-spline Smoothing

Estimation of growth curves or item response curves often involves monotone data smoothing. Methods that have been studied in the literature tend to be either less exible or more diicult to compute when constraints such as monotonicity are incorporated. Built upon the ideas of Ramsay (1988) and Koenker, Ng and Portnoy (1994), we propose monotone B-spline smoothing based on L 1 optimization. It inherits the desirable properties of spline approximations and the computational eeciency of linear programs. The constrained t is similar to the unconstrained estimate in terms of computational complexity and asymptotic rate of convergence. Through applications to some real and simulated data we show that the method is useful in a variety of applications. The basic ideas utilized in monotone smoothing can be useful in some other constrained function estimation problems. The authors thank the Editor, the Associate Editor and two referees for encouraging and helpful comments and suggestions.