An algorithm for the estimation of a regression function by continuous piecewise linear functions
- 160 Downloads
The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L 2 risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones.
KeywordsNonsmooth optimization Nonparametric regression Subdifferential Semismooth functions
Unable to display preview. Download preview PDF.
- 1.Bagirov, A.M.: Minimization methods for one class of nonsmooth functions and calculation of semi-equilibrium prices. In: Eberhard, A., et al. (eds.) Progress in Optimization: Contribution from Australia, pp. 147–175. Kluwer Academic, Dordrecht (1999) Google Scholar
- 15.The R Project for Statistical Computing. Available on: www.r-project.org