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Model Misspecification

In: Linear Model Theory

Author

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  • Dale L. Zimmerman

    (University of Iowa, Department of Statistics and Actuarial Science)

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.

Suggested Citation

  • Dale L. Zimmerman, 2020. "Model Misspecification," Springer Books, in: Linear Model Theory, chapter 12, pages 279-300, Springer.
  • Handle: RePEc:spr:sprchp:978-3-030-52063-2_12
    DOI: 10.1007/978-3-030-52063-2_12
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