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CONTINUOUS PIECEWISE LINEAR FUNCTIONS

Published online by Cambridge University Press:  14 December 2005

CHARALAMBOS D. ALIPRANTIS ,
DAVID HARRIS  and
RABEE TOURKY
CHARALAMBOS D. ALIPRANTIS
Affiliation:
Purdue University
DAVID HARRIS
Affiliation:
The University of Melbourne
RABEE TOURKY
Affiliation:
Purdue University and The University of Melbourne
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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∈J is a finite family of finite sets.

Type
MD SURVEY
Information
Macroeconomic Dynamics , Volume 10 , Issue 1 , February 2006 , pp. 77 - 99
Copyright
© 2006 Cambridge University Press

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References

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