Cobs

Qualitatively constrained smoothing via linear programming

Xuming He, Pin T Ng

Research output: Contribution to journalArticle

67 Citations (Scopus)

Abstract

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 attempt to 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 S-plus users. Recent work of He & Shi (1998) considered a special case and showed that the L1 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.

Original languageEnglish (US)
Pages (from-to)315-337
Number of pages23
JournalComputational Statistics
Volume14
Issue number3
StatePublished - 1999
Externally publishedYes

Fingerprint

Spline Smoothing
B-spline
Splines
Linear programming
Smoothing
Smoothing Algorithm
Smoothing Techniques
Optimal Rate of Convergence
User Interaction
Real-world Applications
Large Data Sets
Smooth function
Automation
Monotonicity
Convexity
Monotone
Projection
Boundary conditions

Keywords

  • Constraint
  • Information criterion
  • Knot selection
  • Linear program
  • Nonparametric regression
  • Regression quantile
  • Smoothing spline

ASJC Scopus subject areas

  • Computational Mathematics
  • Statistics and Probability

Cite this

Cobs : Qualitatively constrained smoothing via linear programming. / He, Xuming; Ng, Pin T.

In: Computational Statistics, Vol. 14, No. 3, 1999, p. 315-337.

Research output: Contribution to journalArticle

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