Examples of L^2-Complete and Boundedly-Complete Distributions
AbstractCompleteness 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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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1801.
Length: 25 pages
Date of creation: May 2011
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Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- D’Haultfoeuille, Xavier, 2011.
"On The Completeness Condition In Nonparametric Instrumental Problems,"
Cambridge University Press, vol. 27(03), pages 460-471, June.
- 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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