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Examples of L2-complete and boundedly-complete distributions

Donald W.K. Andrews

Journal of Econometrics, 2017, vol. 199, issue 2, 213-220

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 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 (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:199:y:2017:i:2:p:213-220

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