Some properties of inferences in misspecified linear models

✍ Scribed by Thomas A. Severini

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 321 KB
• Volume: 40
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00082-0

✦ Synopsis

Let Y denote an n x 1 vector of observations such that Y = # + a~ where /~ is an unknown n x 1 vector, a > 0 is an unknown parameter, and ~ is an n x 1 vector of independent standard normal random variables. A linear regression analysis is often based on a model for # such as /t =X/~ where X is a known n × p matrix of independent variables and ]~ is a p × 1 vector of unknown parameters. When the assumption that/~ =X]~ for some fl holds, the results of the analysis can be interpreted as applying to #, the mean of Y. In this paper, the properties of inferences based on the model # =X/~ are considered without assuming that the model holds. It is shown that many of the usual properties continue to hold, although with respect to /~*, the vector of form X/~ closest to /~, rather than with respect to #. Hence, the results of a linear regression analysis have a certain type of validity that applies whether or not the model is correctly specified.