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Linear Regression Models under Conditional Independence Restrictions
Author(s) -
Causeur David,
Dhorne Thierry
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00355
Subject(s) - mathematics , estimator , statistics , completeness (order theory) , conditional independence , context (archaeology) , linear regression , regression analysis , independence (probability theory) , conditional probability distribution , econometrics , mathematical analysis , paleontology , biology
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.