Cumulative Distribution Estimation via Control Theoretic Smoothing Splines

  • Janelle K. Charles
  • Shan Sun
  • Clyde F. Martin


In this paper, we explore the relationship between control theory and statistics. Specifically, we consider the use of cubic monotone control theoretic smoothing splines in estimating the cumulative distribution function (CDF) defined on a finite interval [0,T]. The spline construction is obtained by imposing an infinite dimensional, non-negativity constraint on the derivative of the optimal curve. The main theorem of this paper states that the optimal curve y(t) is a piecewise polynomial of known degree with y(0) = 0 and y(T) = 1. The solution is determined through dynamic programming which takes advantage of a finite reparametrization of the problem.


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Copyright information

© Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Janelle K. Charles
    • 1
  • Shan Sun
    • 2
  • Clyde F. Martin
    • 1
  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA

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