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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

Y.A. Abramovich and C.D. Aliprantis 2002a An invitation to operator theory, vol. 50 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society.
Y.A. Abramovich and C.D. Aliprantis 2002b Problems in operator theory, vol. 51 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society.
C.D. Aliprantis and K.C. Border 1999 Infinite-dimensional analysis: a hitchhiker's guide. Berlin: Springer-Verlag.
C.D. Aliprantis and O. Burkinshaw 2003 Locally solid Riesz spaces with applications to economics, vol. 105 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.
C.D. Aliprantis, D. Harris, and R. Tourky 2006 Riesz estimators. Journal of Econometrics, Forthcoming.Google Scholar
A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G.M. Ziegler 1999 Oriented matroids, vol. 46 of Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press.
D.J. Brown, C.B. Huijsmans, and B. de Pagter 1991 Approximating derivative securities in f-algebras, in C.D. Aliprantis, K.C. Border, and W.A.J. Luxemburg, eds., Positive operators, Riesz Spaces, and Economics, Studies in Economic Theory, Vol. 2, pp. 171–177. Springer-Verlag, New York and Heidelberg.
W.A.J. Luxemburg and A. C. Zaanen 1971 Riesz spaces, Vol. I. Amsterdam: North-Holland Publishing.
S. Ovchinnikov 2002 Max-min representation of piecewise linear functions. Beirtrage zur Algebra und Geometrie 43 (1), 297– 302.Google Scholar
H.H. Schaefer 1974 Banach lattices and positive operators, vol. 215 of Die Grundlehren der mathematischen Wissenschaften, New York: Springer-Verlag. Band 215.