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    Adeeb, S. and Troitsky, V. G. 2016. Locally piecewise affine functions and their order structure. Positivity,


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CONTINUOUS PIECEWISE LINEAR FUNCTIONS

  • CHARALAMBOS D. ALIPRANTIS (a1), DAVID HARRIS (a2) and RABEE TOURKY (a3)
  • DOI: http://dx.doi.org/10.1017/S1365100506050103
  • Published online: 01 February 2006
Abstract

The paper studies the function space of continuous piecewise linear functions in the space of continuous functions on the m-dimensional Euclidean space. It also studies the special case of one dimensional continuous piecewise linear functions. The study is based on the theory of Riesz spaces that has many applications in economics. The work also provides the mathematical background to its sister paper Aliprantis, Harris, and Tourky (2006), in which we estimate multivariate continuous piecewise linear regressions by means of Riesz estimators, that is, by estimators of the the Boolean form

where X=(X1, X2, …, Xm) is some random vector, {Ej}jJ is a finite family of finite sets.

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Corresponding author
Address correspondence to Charalambos D. Aliprantis, Department of Economics, Purdue University, West Lafayette, IN 47907-1310, USA; e-mail: aliprantis@mgmt.purdue.edu.
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Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
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