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Linear Regression Models under Conditional Independence Restrictions

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  • David Causeur
  • Thierry Dhorne

Abstract

Maximum likelihood estimation is investigated in the context of linear regression models under partial independence restrictions. These restrictions aim to assume a kind of completeness of a set of predictors Z in the sense that they are sufficient to explain the dependencies between an outcome Y and predictors X: ℒ(Y|Z, X) = ℒ(Y|Z), where ℒ(·|·) stands for the conditional distribution. From a practical point of view, the former model is particularly interesting in a double sampling scheme where Y and Z are measured together on a first sample and Z and X on a second separate sample. In that case, estimation procedures are close to those developed in the study of double‐regression by Engel & Walstra (1991) and Causeur & Dhorne (1998). Properties of the estimators are derived in a small sample framework and in an asymptotic one, and the procedure is illustrated by an example from the food industry context.

Suggested Citation

  • David Causeur & Thierry Dhorne, 2003. "Linear Regression Models under Conditional Independence Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 637-650, September.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:3:p:637-650
    DOI: 10.1111/1467-9469.00355
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