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

Donald W. K. Andrews ()

No 1801, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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.

Keywords: Bivariate distribution; Bounded completeness; Canonical correlation; Completeness; Identification; Measurement error; Nonparametric instrumental variable regression (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2011-05
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