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Shape-Constrained Estimation Using Nonnegative Splines

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Tags: Shape-constrained, Nonnegative polynomials, Second-order Programming

This note is for Papp, D., & Alizadeh, F. (2014). Shape-Constrained Estimation Using Nonnegative Splines. Journal of Computational and Graphical Statistics, 23(1), 211–231.

a general framework that treats estimation problems in a unified manner

applications of the approach

  • compute optimal spline estimators for regression, density estimation, and arrival rate estimation problems
  • can handle multiple simultaneous shape constraints
  • based on a characterization of nonnegative polynomials that leads to semdefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problem.
  • these formulation extend and generalize previous approaches in the literature, including those with piecewise linear and B-spline estimators
  • also consider a simpler approach in which nonnegative coefficients in a nonnegative basis

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