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

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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.

Suggested Citation

  • Donald W.K. Andrews, 2011. "Examples of L^2-Complete and Boundedly-Complete Distributions," Cowles Foundation Discussion Papers 1801, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1801
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    More about this item

    Keywords

    Bivariate distribution; Bounded completeness; Canonical correlation; Completeness; Identification; Measurement error; Nonparametric instrumental variable regression;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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