On the Completeness Condition in Nonparametric Instrumental Problems
Xavier D’Haultfœuille
Abstract
Open-access reader
Xavier D’Haultfœuille
Abstract
Open-access reader
The notion of completeness between two random variables has been consideredrecently to provide identification in nonparametric instrumental problems. This conditionis quite abstract, however, and characterizations have been obtained only inspecial cases. The aim of this paper is to provide general sufficient conditions toachieve completeness or bounded completeness. The difference between these twonotions is stressed, and implications for the nonparametric instrumental regressionare given.
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The notion of completeness between two random variables has been consideredrecently to provide identification in nonparametric instrumental problems. This conditionis quite abstract, however, and characterizations have been obtained only inspecial cases. The aim of this paper is to provide general sufficient conditions toachieve completeness or bounded completeness. The difference between these twonotions is stressed, and implications for the nonparametric instrumental regressionare given.
Key concepts: Completeness (order theory), Nonparametric statistics, Instrumental variable, Bounded function, Mathematics, Identification (biology), Nonparametric regression, Calculus (dental)