COBS: Qualitatively Constrained Smoothing via Linear Programming
Popular smoothing techniques generally have a difficult time
accommodating qualitative constraints like monotonicity, convexity or
boundary conditions on the fitted function. In this paper we bring the
problem of constrained spline smoothing to the foreground and describe the
details of a constrained B-spline smoothing (COBS) algorithm that is being
made available to Splus users. Recent work of He and Shi (1996) considered a
special case and showed that the $L_1$ projection of a smooth function
into the space of B-splines provides a monotone smoother that is flexible,
efficient and achieves the optimal rate of convergence. Several options and
generalizations are included in COBS: it can handle small or large data sets
either with user interaction or full automation. Three examples are provided
to show how COBS works in a variety of real-world applications.
- To obtain a postscript copy of the article, click here.
- To obtain a PDF version of the article, click here.
- The algorithm in Fortran, C and Splus for the Unix environment
can be downloaded by clicking here.
This is an alpha version. Do not distribute without the explicit consent
of its owners. We would appreciate feedbacks from you.
Please kindly report bugs or problems to Pin.Ng@nau.edu