Model Misspecification

Dale L. Zimmerman
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Dale L. Zimmerman: University of Iowa, Department of Statistics and Actuarial Science

Chapter 12 in Linear Model Theory, 2020, pp 279-300 from Springer

Abstract: Abstract Beginning in Chap. 7 , we derived least squares estimators of estimable functions and estimators of residual variance corresponding to several linear models, and we derived various sampling properties of those estimators. With few exceptions, the sampling properties were derived under the same models that the estimators were derived. For example, it was established (in Theorems 7.2.1 and 7.2.2 ) that the ordinary least squares estimator of an estimable function c Tβ in a Gauss–Markov model with model matrix X is unbiased and has variance σ 2c T(X TX)−c under that model. What happens to these properties of the ordinary least squares estimator if the model is incorrectly specified? Answering this question and others like it is the primary objective of this chapter.

Date: 2020
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DOI: 10.1007/978-3-030-52063-2_12

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