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Examples of L2-complete and boundedly-complete distributions
- Andrews, Donald W.K.
- Journal of econometrics 2017 v.199 no.2 pp. 213-220
- econometric models, economic analysis, economic theory
- 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.