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Examples of L2-Complete and Boundedly-Complete Distributions

26 Pages Posted: 14 May 2011 Last revised: 3 Jun 2011

Donald W. K. Andrews

Yale University - Cowles Foundation

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

Andrews, Donald W. K., Examples of L2-Complete and Boundedly-Complete Distributions (May 13, 2011). Cowles Foundation Discussion Paper No. 1801. Available at SSRN:

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

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