Chapter 4 Linear Models

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For A a symmetric matrix we have :And assuming that H T H is invertible :Which is exactly :

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For A a symmetric matrix we have :And assuming that H T H is invertible :Which is exactly :

The MVU estimator of Θ and its covariance matrixTheorem : Minimum Variance Unbiased Estimator for the<strong>Linear</strong> ModelAs illustrated in the figure bellow it is clear that an infinitenumber of choices can be made for A and B that will result inthe same observations or given a noiseless x, Θ is not unique.Although rarely occurring in practice, this degeneracysometimes nearly occurs when H T H is ill-conditioned.

Page 1 and 2: Chapter 4Linear ModelsA.T.S.P.Andre
Page 3 and 4: Definition and PropertiesThe linear
Page 5: H is a known matrix of dimension Nx

Chapter 4 Linear Models

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