Macroeconomic Dynamics



MD SURVEY

CONTINUOUS PIECEWISE LINEAR FUNCTIONS


CHARALAMBOS D. ALIPRANTIS a1c1, DAVID HARRIS a2 and RABEE TOURKY a3
a1 Purdue University
a2 The University of Melbourne
a3 Purdue University and The University of Melbourne

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}j[set membership]J is a finite family of finite sets.


Correspondence:
c1 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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