Linear Regression Models under Conditional Independence Restrictions

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": <scriptface>L</scriptface>("Y"|"Z", "X") = <scriptfac e>L</scriptface>("Y"|"Z"), where <scriptface>L</scriptface>(·|·) 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. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..