Journal Article

Monotone B-Spline Smoothing

Xuming He and Peide Shi
Journal of the American Statistical Association
Vol. 93, No. 442 (Jun., 1998), pp. 643-650
DOI: 10.2307/2670115
https://www.jstor.org/stable/2670115
Page Count: 8
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Monotone B-Spline Smoothing
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Abstract

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 on the ideas of Koenker, Ng, and Portnoy and Ramsay, we propose monotone B-spline smoothing based on L1 optimization. This method 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.