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Examples of L^2-Complete and Boundedly-Complete Distributions

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Completeness and bounded-completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non-classical measurement error models. However, distributions that are known to be complete or boundedly complete are somewhat scarce. In this paper, we consider an L^2-completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L^2-complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L^2-incomplete distributions also are provided.

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File URL: http://cowles.econ.yale.edu/P/cd/d18a/d1801.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1801.

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Length: 25 pages
Date of creation: May 2011
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Handle: RePEc:cwl:cwldpp:1801

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Bivariate distribution; Bounded completeness; Canonical correlation; Completeness; Identification; Measurement error; Nonparametric instrumental variable regression;

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  1. Xavier d'Haultfoeuille, 2006. "On the Completeness Condition in Nonparametric Instrumental Problems," Working Papers 2006-32, Centre de Recherche en Economie et Statistique.
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