Examples of L2-Complete and Boundedly-Complete Distributions
Donald W. K. Andrews
Yale University - Cowles Foundation
May 13, 2011
Cowles Foundation Discussion Paper No. 1801
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.
Number of Pages in PDF File: 26
Keywords: Bivariate distribution, Bounded completeness, Canonical correlation, Completeness, Identification, Measurement error, Nonparametric instrumental variable regression
JEL Classification: C14
Date posted: May 14, 2011 ; Last revised: June 3, 2011