Linear Regression Models under Conditional Independence Restrictions

Authors: Causeur D.¹; Dhorne T.²

Source: Scandinavian Journal of Statistics, Volume 30, Number 3, September 2003 , pp. 637-650(14)

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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.

Keywords: double sampling; incomplete data; linear regression model

Document Type: Research article

DOI: http://dx.doi.org/10.1111/1467-9469.00355

Affiliations: 1: ENSA de Rennes, CREST-ENSAI, France 2: SABRES, Université de Bretagne Sud, France

Publication date: 2003-09-01