26 Pages Posted: 14 May 2011 Last revised: 3 Jun 2011
Date Written: May 13, 2011
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 L2-completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L2-complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L2-incomplete distributions also are provided.
Keywords: Bivariate distribution, Bounded completeness, Canonical correlation, Completeness, Identification, Measurement error, Nonparametric instrumental variable regression
JEL Classification: C14
Suggested Citation: Suggested Citation
Andrews, Donald W. K., Examples of L2-Complete and Boundedly-Complete Distributions (May 13, 2011). Cowles Foundation Discussion Paper No. 1801. Available at SSRN: https://ssrn.com/abstract=1840552