Monotone B-Spline Smoothing
提出一种基于L1优化的单调B样条平滑方法，用于增长曲线或项目反应曲线的估计，兼具样条逼近的优良性质和线性规划的计算效率。
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 flexible or more difficult 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 efficiency of linear programs. The constrained fit 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. KEY WORDS: B-spline, constraints, information criterion, least absolute deviation, linear programming, median, monotone...